Morrison's friends Elton John and David Furnish announced the news during John's White Tie and Tiara Ball to benefit his AIDS Foundation in London Thursday.
"Matt's friends absolutely adore Renee!" a source told the magazine. "They have never seen Matt happier than when he is with her. She is super supportive of his career and also works hard on her own. She is such a great girl and they are awesome together."
The report did not say when or where Morrison and Puente plan to marry.
Celebrity Breakups and divorces of 2014 [PHOTOS]