The 52-year-old attended a special screening of his latest film, The Monuments Men, at the White House on February 18 with President Barack Obama.

As his personal guest, he brought along British lawyer Amal Alamuddin, and according to a source the couple were very cosy with each other.

"His arm was around her shoulder and she had hers around his," an observer told People Magazine. "They just seemed very, very together. They were stuck like glue.”

Eternal bachelor George split from Stacy Keibler in July last year.

He has previously romanced model Lisa Snowden and Italian actress Elisabetta Canalis.

George was also married to actress Talia Balsam from 1989 until they divorced in 1993.

But according to onlookers, the Gravity actor seemed smitten with Amal.

“They were holding hands," Harry Ettlinger, 88, one of the World War II soldiers whose efforts to recover stolen art from the Nazis inspired the film, told the publication.

“[Amal] is a beautiful lady, I said to myself, 'George, you did a lot of good things and you sure know how to pick them!'"

After the screening, Amal – who represents WikiLeaks founder Julian Assange – joined George and two of his co-stars in the film, Bill Murray and Matt Damon, for a nightcap in a bar at the Willard Hotel.

Rumours of the two dating first started in October, when they were seen dining together at London's Berners Tavern.

George denied the reports at the time and in December he told W magazine that when it comes to the love of his life, "I haven't met her yet."