diff --git a/.github/workflows/docs.yaml b/.github/workflows/docs.yaml
index a746ae6de3..23b8d7f909 100644
--- a/.github/workflows/docs.yaml
+++ b/.github/workflows/docs.yaml
@@ -3,7 +3,10 @@ name: Deploy the documentation
 on:
   push:
     branches:
+      # For bleeding-edge documentation
       - develop
+      # For documentation specific to a release
+      - 'release-v*'
 
   workflow_dispatch:
 
@@ -22,6 +25,7 @@ jobs:
       - name: Build the documentation
         run: mdbook build
 
+      # Deploy to the latest documentation directories
       - name: Deploy latest documentation
         uses: peaceiris/actions-gh-pages@068dc23d9710f1ba62e86896f84735d869951305 # v3.8.0
         with:
@@ -29,3 +33,32 @@ jobs:
           keep_files: true
           publish_dir: ./book
           destination_dir: ./develop
+
+      - name: Get the current Synapse version
+        id: vars
+        # The $GITHUB_REF value for a branch looks like `refs/heads/release-v1.2`. We do some
+        # shell magic to remove the "refs/heads/release-v" bit from this, to end up with "1.2",
+        # our major/minor version number, and set this to a var called `branch-version`.
+        #
+        # We then use some python to get Synapse's full version string, which may look
+        # like "1.2.3rc4". We set this to a var called `synapse-version`. We use this
+        # to determine if this release is still an RC, and if so block deployment.
+        run: |
+          echo ::set-output name=branch-version::${GITHUB_REF#refs/heads/release-v}
+          echo ::set-output name=synapse-version::`python3 -c 'import synapse; print(synapse.__version__)'`
+
+      # Deploy to the version-specific directory
+      - name: Deploy release-specific documentation
+        # We only carry out this step if we're running on a release branch,
+        # and the current Synapse version does not have "rc" in the name.
+        #
+        # The result is that only full releases are deployed, but can be
+        # updated if the release branch gets retroactive fixes.
+        if: ${{ startsWith( github.ref, 'refs/heads/release-v' ) && !contains( steps.vars.outputs.synapse-version, 'rc') }}
+        uses: peaceiris/actions-gh-pages@v3
+        with:
+          github_token: ${{ secrets.GITHUB_TOKEN }}
+          keep_files: true
+          publish_dir: ./book
+          # The resulting documentation will end up in a directory named `vX.Y`.
+          destination_dir: ./v${{ steps.vars.outputs.branch-version }}
diff --git a/changelog.d/10198.doc b/changelog.d/10198.doc
new file mode 100644
index 0000000000..8d1aeab1a7
--- /dev/null
+++ b/changelog.d/10198.doc
@@ -0,0 +1 @@
+Deploy a snapshot of the documentation website upon each new Synapse release.