George Clooney and Amal Alamuddin Are Engaged

His bachelor days are over!

George Clooney and Amal Alamuddin are engaged.

A source with knowledge of the situation confirms Clooney popped the question and exclusively tells PEOPLE, “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 engagement happened “not that long ago, I think,” the source adds, and the couple don’t appear to have wedding plans in the works – yet.

On Thursday, the pair were spotted at Malibu hot spot Nobu with Cindy Crawford and husband Rande Gerber, who are longtime pals of Clooney’s. At the dinner, Alamuddin had a conspicuous ring on her left ring finger, a different source tells PEOPLE.

In addition, two sources say that witnesses at another L.A. restaurant, Craig’s, reported seeing the pair apparently celebrating their engagement with friends on Wednesday night, with Alamuddin sporting a “huge ring,” according to one.

A rep for the actor has only said, “I don’t comment on my client’s personal life.”

Clooney, 52, and Alamuddin, 36, a British attorney who specializes in international law and human rights, were first photographed stepping out together in London in October. The two have since been spotted embarking on romantic, globe-trotting jaunts.

In March, the two went on a trip to Tanzania, where they were snapped getting cozy during a safari, and they also visited the Seychelles.

A few days later, the couple stepped out together in New York City for dinner at a French restaurant.

Earlier this year, a source who has worked with Clooney, told PEOPLE: “He’s with someone who is a very accomplished attorney. She isn’t someone who is pursuing a career in acting or entertainment. She’s on his level.”

• Reporting by PERNILLA CEDENHEIM, JENNIFER GARCIA, GABRIELLE OLYA and ELIZABETH LEONARD