Lamar Odom is ready to sign his divorce papers.

The basketball star's wife, Khloe Kardashian, filed court documents to legally dissolve their four-year marriage in December, following months of rumors he was addicted to cocaine and cheated on her multiple times, and he has finally realized he won't be able to win her back.

"Lamar finally gets it, his marriage to Khloe is over," a source said.

The 34-year-old athlete is expected to formally submit a response to the Keeping Up with the Kardashians star's divorce petition in the next few weeks, after hearing she "adores" her new beau, French Montana. "There was a time when Lamar said he would never give up on getting back together with Khloe, but he recognizes she has obviously moved on. He will tell his attorney to submit a response to Khloe's divorce petition. It isn't expected to be a long drawn out divorce, since there is an iron clad prenup in place," the source said.

Lamar is said to be very upset that the 29-year-old beauty has moved on with the "Pop That" rapper, despite rumors he is spending time with his ex-girlfriend, Liza Morales, with whom he has children, Destiny, 15, and 11-year-old Lamar Jr. But the source insisted, "It's family time only and there is no romance involved between Lamar and Liza. Liza is extremely supportive of Lamar's continued sobriety."