Crowds are usually capped at 80,000 for transport network capacity reasons but an attendance of 90,000 is expected for the contest in which Joshua's IBF title and the vacant WBA Super and IBO heavyweight belts are up for grabs.
It would match the record 90,000 attendance for the Len Harvey versus Jock McAvoy bout at London's White City in 1939.
"(London Mayor) Sadiq (Khan) urged me to bring the biggest fights to the city and I'm delighted to have the biggest fight in British boxing history at Wembley," Eddie Hearn told the BBC.
London 2012 Olympic champion Joshua has taken the division by storm since turning professional, winning all his 18 fights by knockout. Former champion Klitschko, who will be 41 in March, has 64 wins and four defeats in his 20-year career.
The Ukrainian was unbeaten for 11 years before losing to Britain's Tyson Fury in 2015.
(Reporting by Martyn Herman, editing by Ed Osmond)
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