The pair were snapped by the Daily Telegraph as they arrived at Sydney International Airport, with what appears to be an engagement ring on Alexis' finger.
Alexis lives in Denpasar, Bali, and met Joel through mutual friends during a trip there.
According to a source close to Joel, he's never looked back since. "When he falls, he falls hard," the insider told the Tele.
After Zero Dark Thirty, Joel appears next in the Australian-produced cop drama, Felony, opposite fellow Aussie Melissa George, and double Oscar nominee Tom Wilkinson.
Check out our slideshow of stars who got married or pregnant in the past 12 or so months:
