Sheen and Mueller on June 10
After more than a year of dating, Charlie Sheen and girlfriend Brooke Mueller are engaged, PEOPLE confirms.
Sheen, 41, first stepped out with Mueller
, 29, a real estate investor, at the Chrysalis Butterfly Ball in Los Angeles in June 2006.
The couple's engagement was first reported by Extra
and was confirmed by a Sheen family friend. According to Extra
, Sheen proposed to Mueller on a Costa Rican beach with a $500,000 engagement ring.
Sheen became free to wed
last November when his marital status to Denise Richards
legally ended. The pair have two daughters, Lola, 2, and Sam, 3.
Richards, 36, has extended an olive branch to Mueller and the women were recently spotted together.
"Denise wants her to feel comfortable," a Richards pal told PEOPLE last year. "She put together a bag with toys for her and the girls (Lola and Sam) along with a card telling her she's glad (Brooke) makes their father so happy."