"Yes, they're engaged," the actor's rep tells PEOPLE. "They're very happy and very much in love. They never announced it because he wanted to be discreet and enjoy the good news privately."
Walsh, 29, a British flight attendant, was pregnant with Grammer's child but suffered a miscarriage in the fall.
Grammer, 55, is going through a divorce from his third wife, Camille, 42, who stars on the Real Housewives of Beverly Hills.
Grammer has two children with Camille, daughter Mason, 8, and Jude, 6, and two older daughters, Spencer, and Greer, from previous relationships.
Reporting by ELIZABETH LEONARD