Sources tell us Pete popped the question to Ariana in the last week ... and she, of course, said yes. The pair started officially dating just over a month ago -- following Ariana's split from rapper Mac Miller.

Things have heated up quickly between the two, with Pete getting two Ariana-inspired tattoos earlier this month.

Both Pete and Ariana are 24 ... it's the first engagement for both of them. Pete's also coming off a recent breakup ... he split with "Curb Your Enthusiasm" creator Larry David's daughter, Cazzie David, recently.

It's unclear exactly when Pete and Ariana met ... she was the musical guest and host for 'SNL' in March 2016.