diff --git a/.azure-pipelines/windows.yml b/.azure-pipelines/windows.yml
new file mode 100644
index 0000000000..ad1b72eb77
--- /dev/null
+++ b/.azure-pipelines/windows.yml
@@ -0,0 +1,45 @@
+
+parameters:
+  name: ''
+  vmImage: ''
+  matrix: []
+
+jobs:
+- job: ${{ parameters.name }}
+  pool:
+    vmImage: ${{ parameters.vmImage }}
+  variables:
+    EXTRA_WHEELS: "https://5cf40426d9f06eb7461d-6fe47d9331aba7cd62fc36c7196769e4.ssl.cf2.rackcdn.com"
+  strategy:
+    matrix:
+      ${{ insert }}: ${{ parameters.matrix }}
+
+  steps:
+    - task: UsePythonVersion@0
+      inputs:
+        versionSpec: '$(PYTHON_VERSION)'
+        addToPath: true
+        architecture: '$(PYTHON_ARCH)'
+    - script: |
+        python -m pip install --upgrade pip setuptools>=30.3.0 wheel
+      displayName: 'Update build tools'
+    - script: |
+        python -m pip install --find-links %EXTRA_WHEELS% numpy scipy matplotlib h5py pydicom
+        python -m pip install nose mock coverage codecov
+      displayName: 'Install dependencies'
+    - script: |
+        python -m pip install .
+        SET NIBABEL_DATA_DIR=%CD%\\nibabel-data
+      displayName: 'Install nibabel'
+    - script: |
+        mkdir for_testing
+        cd for_testing
+        cp ../.coveragerc .
+        nosetests --with-doctest --with-coverage --cover-package nibabel nibabel
+      displayName: 'Nose tests'
+    - script: |
+        cd for_testing
+        codecov
+      displayName: 'Upload To Codecov'
+      env:
+        CODECOV_TOKEN: $(CODECOV_TOKEN)
diff --git a/appveyor.yml b/appveyor.yml
deleted file mode 100644
index 796c74a7da..0000000000
--- a/appveyor.yml
+++ /dev/null
@@ -1,46 +0,0 @@
-# vim ft=yaml
-# CI on Windows via appveyor
-
-environment:
-
-  matrix:
-    - PYTHON: C:\Python27
-    - PYTHON: C:\Python27-x64
-    - PYTHON: C:\Python34
-    - PYTHON: C:\Python34-x64
-    - PYTHON: C:\Python35
-    - PYTHON: C:\Python35-x64
-    - PYTHON: C:\Python36
-    - PYTHON: C:\Python36-x64
-    - PYTHON: C:\Python37
-    - PYTHON: C:\Python37-x64
-
-install:
-  # Prepend newly installed Python to the PATH of this build (this cannot be
-  # done from inside the powershell script as it would require to restart
-  # the parent CMD process).
-  - SET PATH=%PYTHON%;%PYTHON%\Scripts;%PATH%
-
-  - python -m pip install --upgrade pip virtualenv
-  - virtualenv --python=python venv
-  - venv\Scripts\activate
-  - python --version
-
-  # Install the dependencies of the project.
-  - pip install --upgrade pip setuptools>=27.0 wheel
-  - pip install numpy scipy matplotlib h5py pydicom
-  - pip install nose mock coverage codecov
-  - pip install .
-  - SET NIBABEL_DATA_DIR=%CD%\nibabel-data
-
-build: false  # Not a C# project, build stuff at the test step instead.
-
-test_script:
-  # Change into an innocuous directory and find tests from installation
-  - mkdir for_testing
-  - cd for_testing
-  - cp ../.coveragerc .
-  - nosetests --with-doctest --with-coverage --cover-package nibabel nibabel
-
-after_test:
-  - codecov
diff --git a/azure-pipelines.yml b/azure-pipelines.yml
new file mode 100644
index 0000000000..cb2612d5c3
--- /dev/null
+++ b/azure-pipelines.yml
@@ -0,0 +1,25 @@
+# Adapted from https://github.com/pandas-dev/pandas/blob/master/azure-pipelines.yml
+jobs:
+- template: .azure-pipelines/windows.yml
+  parameters:
+    name: Windows
+    vmImage: vs2017-win2016
+    matrix:
+      py35-x86:
+        PYTHON_VERSION: '3.5'
+        PYTHON_ARCH: 'x86'
+      py35-x64:
+        PYTHON_VERSION: '3.5'
+        PYTHON_ARCH: 'x64'
+      py36-x86:
+        PYTHON_VERSION: '3.6'
+        PYTHON_ARCH: 'x86'
+      py36-x64:
+        PYTHON_VERSION: '3.6'
+        PYTHON_ARCH: 'x64'
+      py37-x86:
+        PYTHON_VERSION: '3.7'
+        PYTHON_ARCH: 'x86'
+      py37-x64:
+        PYTHON_VERSION: '3.7'
+        PYTHON_ARCH: 'x64'