Canadian Kirk Johnson was set to fight Lewis at the Staples Center but was forced to back out when an MRI revealed a partially torn chest muscle suffered while sparring.
With a 32-1 record, including 31 knockouts, the six foot seven inch Klitschko is the top-rated contender by the WBC and was scheduled to face undefeated Cedric Boswell on the undercard of the Lewis-Johnson bout.
"This has been a life-long dream of mine to fight Lennox Lewis," Klitschko said. "I am very excited about the opportunity to fight him... It is going to be a great fight."
Klitschko, 31, and Lewis were expected to meet some time later this year but the fight has been brought forward by Johnson's injury.
The 37-year-old Lewis, with 40 wins and just two defeats, including 31 knockouts, has not fought since an eighth-round knockout of former champion Mike Tyson last June.
"The fight will not go the distance," Lewis said. "I do not get paid for overtime. Klitschko has been calling me out for some time, but he is in big trouble.
"He should be careful what he wishes for. On June 21, he is going to find out what it is like to be in with an A-class world champion."
Klitschko has won five fights since his only loss to IBF heavyweight champion Chris Byrd in April 2000.
Most recently, he recorded a 10th-round technical knockout over Larry Donald in November.
