The 'Shrek' star proposed last Wednesday (25.07.07) with a "massive" Cartier yellow diamond engagement ring.
Edmonds proudly showed off the ring at lunch with friends the next day at the W Hotel in Westwood, California.
A source said: "She looked very happy. She was proudly showing off the ring. They're very adorable together, very happy. It will be a private wedding. Something low key, but very romantic."
Murphy and Edmonds are said to be planning to tie the knot before the end of the year.
Edmonds' representative said: "Tracey and Eddie were engaged last Wednesday. They are both very much in love and are excited about spending the rest of their lives together."