The award-winning comedian was confirmed as part of a comedy bill for the Dorset event which also includes Marcus Brigstocke and Milton Jones.
Whitehall said: "I'm really looking forward to Camp Bestival in July. It's the only festival I am doing this year and I know it's going to be brilliant."
Further lineup additions include reggae cover band Easy Star All-Stars, BBC radio DJ Mistajam and Shrek The Musical.
Festival curator Rob Da Bank added: "Easy Star All-Stars are one of my favourite festival acts with their reggae versions of Radiohead and Pink Floyd... and perhaps most excitingly for the young at heart, Shrek is comin' to Dorset. Yee-haa!"
Mark Ronson & The Business Intl, Blondie and Laura Marling have already been confirmed to play the festival, which takes place at Lulworth Castle between July 29 and July 31.
Primal Scream will also perform their Mercury Prize-winning album Screamadelica in its entirety.