Katy Perry and Russell Brand before their divorce
Katy Perry and Russell Brand have agreed … Katy will stay in the couple’s $6.5 million Hollywood Hills mansion and Russell will move out …

Sources close to the couple tell us … the moving process is already under way and most of Russell’s stuff is already out of the home.

We’re told … the two are on reasonably good terms with each other, considering they just broke up … and the decision over the house went pretty smoothly.

As we previously reported, the couple purchased the home together just a few months ago. We’re guessing if Katy wants to stay in the home long term, she’ll most likely have to cut Russell a big, fat check.