Is it possible to download an old APK for my app from Google Play?

Latest Update:

Go to

Developer Console => App releases => Production (Manage Production) => Release history => Select the version that you want => Click on Download button.

Your account should be granted with full permissions, otherwise the download button will be hidden.

Original Answer

Go to

Developer Console => Manage Releases => Artifact Library = > Archived Artifacts

You get the option to download the previous releases.

Update:

Go to

Developer Console => App releases => Artifact library => Check the version code/name you wanna download and click the download button at the right.

** Update: **

Developer Console => App releases => Production (Manage Production) => Download arrow.

THE ANSWER IS OUTDATED. NOW THIS IS POSSIBLE, CHECK @tesla's AND @olleh's ANSWERS.

FOR THE NEW 2020 GOOGLE PLAY CONSOLE, SEE ANSWER FROM @IonicBurger

No, unfortunately.

The Android Developer Console is a real disaster, everywhere you look there is something that needs to be fixed or improved, being this issue you mention one of them. Unfortunately for the time being you're out of luck. Unless Google enables this, you cannot download old APKS's. I suppose you could recompile the old code, but I guess you don't have that either and that's why you are here :-)

Now it is possible. They added "Manage Releases" tab to Google Play Developer Console. From Artifact Library under the Release Management tab, you can download your app's APK.

You need to have the necessary permissions to see the download button next to your artifacts. If in doubt, try the root account.