Iggy Azalea is engage as Lakers BF proposes at BDay party

Iggy Azalea is officially on her way to becoming Mrs. Swaggy P -- her NBA star boyfriend Nick Young popped the question ... and she said, "Yes!"

It all went down at Nick Young's 30th birthday party Monday night -- with the L.A. Lakers star getting down on one knee and busting out a fat diamond ring ... according to hip hop insider Karen Civil.

The two started dating back in 2013 -- for their first date, Nick took her to a Target to go shoppping.

From there, they hit it off quickly -- with Nick once taking her home from a club and bragging, "What I'm about to do with this shouldn't be legal!"

Soooo ... congrats!!!