Kiltschko (32-1, 31 KOs) is expected to face WBC champion Lewis later this year.
The WBC mandatory challenger will fight on the undercard when Lewis takes on Kirk Johnson of Canada. Lewis was trying to get Mike Tyson in a co-feature before staging a rematch with the former champion.
His title will not be on the line against Johnson, meaning Klitschko will fight for it later this year.
The 31-year-old Klitschko has won five bouts since his only loss to IBF heavyweight champion Chris Byrd in April 2000. Most recently, Klitschko recorded a 10th-round technical knockout of Larry Donald in November.
"I'm excited to box in L.A. first, and then against 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 taken place. He has not fought in the United States since August 1998, when he stopped Ricardo Kennedy in the first round.
While the 6-3 Boswell (21-0, 16 KOs) is undefeated, he has not beaten any noteworthy opponents. He has stopped four of five opponents since 2002 after a two-year hiatus.
"No question, he is dangerous," said Klitschko's trainer, Fritz Sudnek. "Somebody who is undefeated and won 16 times inside the distance can punch hard. We have to wait and see whether he will fight as courageous against Vitali. We are definitely aware of Boswell."
Klitschko should be especially wary, after his younger brother, Wladimir Klitschko (40-2, 37 KOs), was upset by an unheralded opponent in his last bout.
Wladimir Klitschko was considered one of the top threats among the heavyweights, but suffered a second-round TKO to journeyman Corrie Sanders in March.
Wladimir Klitschko, 26, is one of two boxers to beat Byrd, recording a unanimous decision in October 2000.