"The couple has never been happier," their rep told People magazine. "They're sharing their joy and excitement with their children and their families."
Burnett reportedly proposed to Downey on a moonlit beach in Zihuatanejo, Mexico, where the couple was spending the holiday weekend.
Burnett and Downey, both 46, met as neighbors in Malibu, Calif., in early 2004.
Downey's daughter, 10-year-old Reilly, is from a previous marriage. Burnett has two sons James, 13, and Cameron, 9, from a previous marriage. All children were reportedly present when the engagement took place.