The UK and Ireland exclusive performance will bring the LA four-piece to a UK festival for the first time since 2007.
The band said: "To headline the Isle of Wight Festival is a once-in-a-lifetime opportunity, following in the footsteps of Jimi Hendrix and the Doors. When we were offered the slot, we jumped at the chance. It will be our only show in the UK/Ireland this year so we intend to make it really special."
John Giddings, the festival's promoter, said: "Finally we've got them. One of the most exciting rock bands of the modern era come to visit and judging by the performances I have seen previously, will be a highlight in the music history of the festival. Rock the Wight."
The Chili Peppers will take the Saturday night headline slot following on from Biffy Clyro and Calvin Harris, who will top the bill on the Friday night of the event, which takes place in Newport between June 12 and 15.
Other acts already announced include Rudimental, the Waterboys, Passenger and The 1975.