Klitschko (32-1, 31 KOs) is the WBC mandatory challenger, and on June 21 will fight on the undercard, when Lewis takes on Kirk Johnson of Canada. Lewis was hoping for a rematch with Mike Tyson, but the former champion said he was not ready to fight Lewis after knocking out Clifford Etienne in less than a minute in February.
Lewis' title will not be on the line against Johnson, and Klitschko's opponent has not yet been announced.
"After the long negotiations I'm more than happy that this case is brought to the rung eventually," said Klaus-Peter Kohl, Klitschko's promoter. "Lennox has proven he's a big champion and a gentleman who takes every big challenge."
Klitschko, 31, has won five bouts since his only loss to IBF heavyweight champion Chris Byrd in April 2000. Most recently, he recorded a 10th-round TKO over Larry Donald in November.
"I'm excited to box in L.A. first and then vs. Lennox Lewis," Klitschko said. "I was sure I'd box for the world title. It had to be Lewis as far as I am concerned. Now, one of my biggest goals in my career is close -- fight a big champion for a big title. I am sure I will convince the American fans with my performance."
The 6-7 1/2 Klitschko resides in Germany, where his last eight fights have been. He has not fought in the United States since August 1998, when he stopped Ricardo Kennedy in the first round.
Wladimir Klitschko (40-2, 37 KOs), Vitali's younger brother, was considered to be one of the top threats among heavyweights, but suffered a second-round TKO loss to journeyman Corrie Sanders in March. Vladimir Klitschko, 26, is the only boxer to beat Byrd, recording a unanimous decision in October 2000.