Miley Cyrus and Liam Hemsworth have worked out all the details of their divorce ... TMZ has learned.

Sources directly connected to Liam and Miley tell TMZ, her lawyer will file legal docs Tuesday declaring the 2 have reached a settlement in their divorce.

The divorce was marked by significant bitterness on both sides, but that seems to have subsided as they decided it's better to move on than fight.

It really wasn't that difficult to ultimately settle up. They have no kids, she'll keep the animals and our sources tell us there's a prenup so dividing property wasn't all that tough.

The lawyers behind the settlement -- disso queen Laura Wasser repping Liam and Judith R. Forman repping Miley -- were able to quietly work through the stumbling blocks and submit the paperwork to the judge.

Liam's the one who filed for divorce back in August, citing irreconcilable differences. The divorce won't become final for 6 months after filing ... so they should be single in March.