diff --git a/changelogs/unreleased/41899-api-endpoint-for-importing-a-project-export.yml b/changelogs/unreleased/41899-api-endpoint-for-importing-a-project-export.yml
new file mode 100644
index 00000000000..29ab7cc7cab
--- /dev/null
+++ b/changelogs/unreleased/41899-api-endpoint-for-importing-a-project-export.yml
@@ -0,0 +1,5 @@
+---
+title: API endpoint for importing a project export
+merge_request: 17025
+author:
+type: added
diff --git a/doc/api/README.md b/doc/api/README.md
index 88710eae4fe..b193ef4ab7f 100644
--- a/doc/api/README.md
+++ b/doc/api/README.md
@@ -43,6 +43,7 @@ following locations:
 - [Pipeline Schedules](pipeline_schedules.md)
 - [Projects](projects.md) including setting Webhooks
 - [Project Access Requests](access_requests.md)
+- [Project import/export](project_import_export.md)
 - [Project Members](members.md)
 - [Project Snippets](project_snippets.md)
 - [Protected Branches](protected_branches.md)
diff --git a/doc/api/project_import_export.md b/doc/api/project_import_export.md
new file mode 100644
index 00000000000..e442442c750
--- /dev/null
+++ b/doc/api/project_import_export.md
@@ -0,0 +1,74 @@
+# Project import API
+
+[Introduced][ce-41899] in GitLab 10.6
+
+[See also the project import/export documentation](../user/project/settings/import_export.md)
+
+## Import a file
+
+```http
+POST /projects/import
+```
+
+| Attribute | Type           | Required | Description                              |
+| --------- | -------------- | -------- | ---------------------------------------- |
+| `namespace` | integer/string | no | The ID or path of the namespace that the project will be imported to. Defaults to the current user's namespace |
+| `file` | string | yes | The file to be uploaded |
+| `path` | string | yes | Name and path for new project |
+
+To upload a file from your filesystem, use the `--form` argument. This causes
+cURL to post data using the header `Content-Type: multipart/form-data`.
+The `file=` parameter must point to a file on your filesystem and be preceded
+by `@`. For example:
+
+```console
+curl --request POST --header "PRIVATE-TOKEN: 9koXpg98eAheJpvBs5tK" --form "path=api-project" --form "file=@/path/to/file" https://gitlab.example.com/api/v4/projects/import
+```
+
+```json
+{
+  "id": 1,
+  "description": null,
+  "name": "api-project",
+  "name_with_namespace": "Administrator / api-project",
+  "path": "api-project",
+  "path_with_namespace": "root/api-project",
+  "created_at": "2018-02-13T09:05:58.023Z",
+  "import_status": "scheduled"
+}
+```
+
+## Import status
+
+Get the status of an import.
+
+```http
+GET /projects/:id/import
+```
+
+| Attribute | Type           | Required | Description                              |
+| --------- | -------------- | -------- | ---------------------------------------- |
+| `id`      | integer/string | yes      | The ID or [URL-encoded path of the project](README.md#namespaced-path-encoding) owned by the authenticated user |
+
+```console
+curl --header "PRIVATE-TOKEN: 9koXpg98eAheJpvBs5tK" https://gitlab.example.com/api/v4/projects/1/import
+```
+
+Status can be one of `none`, `scheduled`, `failed`, `started`, or `finished`.
+
+If the status is `failed`, it will include the import error message under `import_error`.
+
+```json
+{
+  "id": 1,
+  "description": "Itaque perspiciatis minima aspernatur corporis consequatur.",
+  "name": "Gitlab Test",
+  "name_with_namespace": "Gitlab Org / Gitlab Test",
+  "path": "gitlab-test",
+  "path_with_namespace": "gitlab-org/gitlab-test",
+  "created_at": "2017-08-29T04:36:44.383Z",
+  "import_status": "started"
+}
+```
+
+[ce-41899]: https://gitlab.com/gitlab-org/gitlab-ce/issues/41899
diff --git a/doc/api/projects.md b/doc/api/projects.md
index 05d2f2af00b..9e649efea9c 100644
--- a/doc/api/projects.md
+++ b/doc/api/projects.md
@@ -1330,6 +1330,10 @@ POST /projects/:id/housekeeping
 
 Read more in the [Branches](branches.md) documentation.
 
+## Project Import/Export
+
+Read more in the [Project import/export](project_import_export.md) documentation.
+
 ## Project members
 
 Read more in the [Project members](members.md) documentation.
diff --git a/doc/user/project/settings/import_export.md b/doc/user/project/settings/import_export.md
index b8f865679a2..dedf102fc37 100644
--- a/doc/user/project/settings/import_export.md
+++ b/doc/user/project/settings/import_export.md
@@ -22,6 +22,7 @@
 >    in the import side is required to map the users, based on email or username.
 >    Otherwise, a supplementary comment is left to mention the original author and
 >    the MRs, notes or issues will be owned by the importer.
+>  - Control project Import/Export with the [API](../../../api/project_import_export.md).
 
 Existing projects running on any GitLab instance or GitLab.com can be exported
 with all their related data and be moved into a new GitLab instance.
diff --git a/lib/api/api.rb b/lib/api/api.rb
index e953f3d2eca..754549f72f0 100644
--- a/lib/api/api.rb
+++ b/lib/api/api.rb
@@ -138,6 +138,7 @@ module API
     mount ::API::PagesDomains
     mount ::API::Pipelines
     mount ::API::PipelineSchedules
+    mount ::API::ProjectImport
     mount ::API::ProjectHooks
     mount ::API::Projects
     mount ::API::ProjectMilestones
diff --git a/lib/api/entities.rb b/lib/api/entities.rb
index 03abc1b95c5..45c737c6c29 100644
--- a/lib/api/entities.rb
+++ b/lib/api/entities.rb
@@ -91,6 +91,13 @@ module API
       expose :created_at
     end
 
+    class ProjectImportStatus < ProjectIdentity
+      expose :import_status
+
+      # TODO: Use `expose_nil` once we upgrade the grape-entity gem
+      expose :import_error, if: lambda { |status, _ops| status.import_error }
+    end
+
     class BasicProjectDetails < ProjectIdentity
       include ::API::ProjectsRelationBuilder
 
diff --git a/lib/api/project_import.rb b/lib/api/project_import.rb
new file mode 100644
index 00000000000..c32e2f26ae3
--- /dev/null
+++ b/lib/api/project_import.rb
@@ -0,0 +1,65 @@
+module API
+  class ProjectImport < Grape::API
+    include PaginationParams
+
+    helpers do
+      def import_params
+        declared_params(include_missing: false)
+      end
+
+      def file_is_valid?
+        import_params[:file] && import_params[:file]['tempfile'].respond_to?(:read)
+      end
+
+      def validate_file!
+        render_api_error!('The file is invalid', 400) unless file_is_valid?
+      end
+    end
+
+    before do
+      forbidden! unless Gitlab::CurrentSettings.import_sources.include?('gitlab_project')
+    end
+
+    resource :projects, requirements: API::PROJECT_ENDPOINT_REQUIREMENTS do
+      params do
+        requires :path, type: String, desc: 'The new project path and name'
+        requires :file, type: File, desc: 'The project export file to be imported'
+        optional :namespace, type: String, desc: "The ID or name of the namespace that the project will be imported into. Defaults to the current user's namespace."
+      end
+      desc 'Create a new project import' do
+        detail 'This feature was introduced in GitLab 10.6.'
+        success Entities::ProjectImportStatus
+      end
+      post 'import' do
+        validate_file!
+
+        Gitlab::QueryLimiting.whitelist('https://gitlab.com/gitlab-org/gitlab-ce/issues/42437')
+
+        namespace = if import_params[:namespace]
+                      find_namespace!(import_params[:namespace])
+                    else
+                      current_user.namespace
+                    end
+
+        project_params = import_params.merge(namespace_id: namespace.id,
+                                             file: import_params[:file]['tempfile'])
+        project = ::Projects::GitlabProjectsImportService.new(current_user, project_params).execute
+
+        render_api_error!(project.errors.full_messages&.first, 400) unless project.saved?
+
+        present project, with: Entities::ProjectImportStatus
+      end
+
+      params do
+        requires :id, type: String, desc: 'The ID of a project'
+      end
+      desc 'Get a project export status' do
+        detail 'This feature was introduced in GitLab 10.6.'
+        success Entities::ProjectImportStatus
+      end
+      get ':id/import' do
+        present user_project, with: Entities::ProjectImportStatus
+      end
+    end
+  end
+end
diff --git a/spec/requests/api/project_import_spec.rb b/spec/requests/api/project_import_spec.rb
new file mode 100644
index 00000000000..eabf9095c13
--- /dev/null
+++ b/spec/requests/api/project_import_spec.rb
@@ -0,0 +1,102 @@
+require 'spec_helper'
+
+describe API::ProjectImport do
+  let(:export_path) { "#{Dir.tmpdir}/project_export_spec" }
+  let(:user) { create(:user) }
+  let(:file) { File.join(Rails.root, 'spec', 'features', 'projects', 'import_export', 'test_project_export.tar.gz') }
+  let(:namespace) { create(:group) }
+  before do
+    allow_any_instance_of(Gitlab::ImportExport).to receive(:storage_path).and_return(export_path)
+
+    namespace.add_owner(user)
+  end
+
+  after do
+    FileUtils.rm_rf(export_path, secure: true)
+  end
+
+  describe 'POST /projects/import' do
+    it 'schedules an import using a namespace' do
+      stub_import(namespace)
+
+      post api('/projects/import', user), path: 'test-import', file: fixture_file_upload(file), namespace: namespace.id
+
+      expect(response).to have_gitlab_http_status(201)
+    end
+
+    it 'schedules an import using the namespace path' do
+      stub_import(namespace)
+
+      post api('/projects/import', user), path: 'test-import', file: fixture_file_upload(file), namespace: namespace.full_path
+
+      expect(response).to have_gitlab_http_status(201)
+    end
+
+    it 'schedules an import at the user namespace level' do
+      stub_import(user.namespace)
+
+      post api('/projects/import', user), path: 'test-import2', file: fixture_file_upload(file)
+
+      expect(response).to have_gitlab_http_status(201)
+    end
+
+    it 'schedules an import at the user namespace level' do
+      expect_any_instance_of(Project).not_to receive(:import_schedule)
+      expect(Gitlab::ImportExport::ProjectCreator).not_to receive(:new)
+
+      post api('/projects/import', user), namespace: 'nonexistent', path: 'test-import2', file: fixture_file_upload(file)
+
+      expect(response).to have_gitlab_http_status(404)
+      expect(json_response['message']).to eq('404 Namespace Not Found')
+    end
+
+    it 'does not schedule an import if the user has no permission to the namespace' do
+      expect_any_instance_of(Project).not_to receive(:import_schedule)
+
+      post(api('/projects/import', create(:user)),
+           path: 'test-import3',
+           file: fixture_file_upload(file),
+           namespace: namespace.full_path)
+
+      expect(response).to have_gitlab_http_status(404)
+      expect(json_response['message']).to eq('404 Namespace Not Found')
+    end
+
+    it 'does not schedule an import if the user uploads no valid file' do
+      expect_any_instance_of(Project).not_to receive(:import_schedule)
+
+      post api('/projects/import', user), path: 'test-import3', file: './random/test'
+
+      expect(response).to have_gitlab_http_status(400)
+      expect(json_response['error']).to eq('file is invalid')
+    end
+
+    def stub_import(namespace)
+      expect_any_instance_of(Project).to receive(:import_schedule)
+      expect(Gitlab::ImportExport::ProjectCreator).to receive(:new).with(namespace.id, any_args).and_call_original
+    end
+  end
+
+  describe 'GET /projects/:id/import' do
+    it 'returns the import status' do
+      project = create(:project, import_status: 'started')
+      project.add_master(user)
+
+      get api("/projects/#{project.id}/import", user)
+
+      expect(response).to have_gitlab_http_status(200)
+      expect(json_response).to include('import_status' => 'started')
+    end
+
+    it 'returns the import status and the error if failed' do
+      project = create(:project, import_status: 'failed', import_error: 'error')
+      project.add_master(user)
+
+      get api("/projects/#{project.id}/import", user)
+
+      expect(response).to have_gitlab_http_status(200)
+      expect(json_response).to include('import_status' => 'failed',
+                                       'import_error' => 'error')
+    end
+  end
+end