The 76-year-old, who left the group in 1992, will be a guest for the first of two gigs at the O2 Arena in London on Sunday.
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.
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 performance aside from a secret warm-up show in Paris last month, have drawn criticism for their huge prices.
Many tickets were priced at £375, and some were being offered for up to £12,000 on resale sites.
However prices appear to have dropped markedly with some selling for below their initial price as the dates approach.
Online ticket marketplace Viagogo has reported that top-tier tickets can now be picked up for just £250 - £125 less than their face value.
A Viagogo spokesman said the lower prices showed the "true value" of the ticket. "We're seeing that, as the gigs draw closer, the reality is people are prepared to pay around £250 to see the Stones," he said.