The 1980s band will perform on the festival's Floating Stage on the Sunday followed by fireworks.
The five-day festival, which features music, comedy, and dance, will be held from 8-12 July at Henley-on-Thames.
In a statement, the band said: "Summer by the Thames at Henley sounds like an offer not to be refused. We can't wait to see everyone there."
Lionel Richie will open the festival, other acts include Jessie J and a philharmonic celebration of American composer and pianist George Gershwin.
About 25,000 people are expected to attend the festival, which started in 1983.
Spandau Ballet will close this year's Henley Festival, organisers have confirmed.