Khloe Kardashian Filing for Divorce From Lamar Odom -- TODAY

Khloe Kardashian is filing for divorce from Lamar Odom ... TODAY ... TMZ has learned.

Sources tell us, Khloe will be citing irreconcilable differences in her legal docs. The split should be pretty cut and dry -- an ironclad prenup which kept all their assets separate ... and no kids.

As we reported, Lamar's bizarre freestyle rap video -- in which he brags about cheating on Khloe -- was the last straw in their crumbling relationship. Immediately after TMZ posted the video last month, Khloe stopped wearing her wedding ring.

The end was a long time coming ... Khloe had expressed dire concerns about the marriage ever since she learned about Lamar's crack addiction earlier this year, but she forestalled divorce for fear he'd OD or worse.

Lamar and Khloe tied the knot in September 2009.