The 'Monuments Men' actor met lawyer Amal Alamuddin at a small charity fundraiser last September and after being instantly attracted to her he resorted to sending her messages online since she refused to take his number.
He emailed her saying: "I think the reported hottest man in the world should meet with the hottest human rights lawyer in the world."
A source told The Daily Mirror newspaper: "At first Amal was playing very hard to get and would not take his phone number, which simply made George even more intrigued.
"In the end he managed to get her email address and began sending her a series of flirty messages. He was very up front and joked about the fact they were both considered the hottest people in their respected professions.
"It was all very tongue in cheek but it got the ball rolling. Amal found it funny, but she still made him wait a few days before replying."
Meanwhile, George, 53, is house hunting in London since Amal, 36, who works at Doughty Street Chambers, will be based in England's capital.
A source added: "George has only known Amal for a few months but with the wedding date set he is now looking for a UK base.
"He wants a place in Richmond because he loves the park and thinks it will be a great place to set up home with Amal.
"She works mainly in London so he will be moving to the UK on a more permanent basis."