The Norway international was out of contract in the summer but, to facilitate his move to the United States, the Tigers have released the player early.
The move to LAFC sees Diomande link up again with coach Bob Bradley after having worked with him at Norwegian club Stabaek.
"We are excited to add Adama to our club," said LAFC general manager John Thorrington. "Adama is a dangerous striker who will add another element to our attack.
"He has top-level international and club experience, and, with his familiarity with Bob, we expect him to contribute immediately. In Adama, we are signing another very good player in the prime of his career."
The 28-year-old had been in and out of the Hull side this season, making just three starts in the Championship with another 13 appearances off the bench.