Burgess showed off her new diamond engagement ring on the red carpet at the iHeartRadio Music Festival at T-Mobile Arena in Las Vegas on Friday.
She also posted an Instagram video in which she and Green stacked their hands on top of those of their children.
“Our latest chapter,” she wrote.
The couple told People.com that they have been engaged for about two months, but haven’t done much planning for their wedding yet.
“We’ve just kind of kept it to ourselves and our family and immediate friends, like people within our sphere and our circle,” Green said.
Burgess added: “We haven’t even talked about it at all. We had such a full busy life with things and four kids at home and we’re in no rush. Honestly, I’m so grateful to be able to say he’s my fiancé, not my boyfriend now.”
The couple are the parents of son Zane Walker, 1.
Green also shares sons Noah Shannon, 10, Bodhi Ransom, 9, and Journey River, 7, with his ex-wife Megan Fox, and son Kassius Lijah, 21, with his ex-girlfriend Vanessa Marcil.