The singer was doing her thing onstage in Munich when she told the crowd at her Friday concert she's getting married to Rich ... flashing her massive engagement ring in the process.

Check out the video from the concert ... Adele is telling a story about how she told someone, "I can't marry you because I'm already getting married" ... and the crowd goes nuts as soon as Adele finishes the sentence -- and shows off the 4-carat diamond ring on THAT finger.

The engagement ring looks like the one Adele's been wearing for a while ... a piece of jewelry that sparked rumors that Rich had finally popped the question.

Now, Adele's confirming recent reports that Rich proposed last month in London ... though it's unclear when they're planning to walk down the aisle.

Adele's been calling herself Rich's wife for a few months now ... it's more of an unofficial title, but seems they're getting to work on making it official. She's also mentioned wanting to start a family together.