The couple, who have been dating since late-last year, recently sparked rumours they're heading for the aisle and now an insider has confirmed their happy news.
A source told People magazine: "George and Amal are trying to keep things very low-key but they also aren't really trying to hide this, it doesn't seem.
"I think it's like they want the people they love to know that this is real, that they plan on being together forever."
The 36-year-old lawyer first fuelled rumours George, 52, had proposed when she was spotted showing off a diamond sparkler on her ring finger as they indulged in sushi at Nobu in Malibu on Thursday (24.04.14).
It is believed the loved-up duo, who are yet to confirm they are even dating, were joined by Cindy Crawford, 48, and actor Edward Norton, 44.
The pair - who were first linked after a dinner date in October - have been getting serious in recent months and were most recently seen at a special screening of George's movie 'Monuments Men' at the White House in February.
An onlooker said at the time: "His arm was around her shoulder and she had hers around his. They just seemed very, very together."
George's romance with Amal came shortly after he split from Stacy Keibler last July, who reportedly ended their relationship because the Hollywood hunk didn't want to settle down and have children.