The Stones will also welcome back guitarist Mick Taylor, who spent five years with the group as a replacement for Brian Jones until he quit in 1974.
The show is the first of five 50 And Counting performances to mark the band's 50th anniversary, with two shows at the O2 and three in New York and Newark, New Jersey.
They are due to play for more than two hours without a support act, with the band promising "a set list packed with hits, classics, and one or two surprises".
Wyman was with the band from their early days until he quit -- going on to perform with his band Rhythm Kings -- and was replaced by Darryl Jones. Taylor was succeeded by Ronnie Wood.
The gigs, which mark the group's return after five years away from live shows, have drawn criticism for their huge prices.
Many tickets were priced at £375 (¤464), and some were on resale sites for up to £12,000 (¤14,800).
However prices appear to have dropped markedly as the dates approach.