George Clooney and Stacy Keibler -- Broke Up Over the Phone

George Clooney and Stacy Keibler phoned in the end of their relationship ... as in, they broke up over the phone while they were half-a-world apart ... TMZ has learned.

Sources close to the couple tell us ... the two had been growing apart over the past 3 months, with George in Europe working on a movie and Stacy in L.A. working on her new TV show.

But with Clooney scheduled to remain in Berlin until December -- Stacy decided she couldn't do the long distance for another 5 months.

One source tells us, "Both sides realized there is no way to have a relationship when you don't see each other."

We're told the two talked out the situation like adults -- and both agreed going their separate ways was best.

So how did George handle it? Like a friggin' gentlemen -- "He was very respectful, adult about the situation ... and they discussed the fact that they were friends before they dated and want to stay friends after."

There are reports that Stacy was pushing GC for kids and that's why the relationship fizzled -- but we're told that couldn't be further from the truth.