The two-part Channel 4 show, called Love for Sale, includes interviews with people who buy and sell sex in locations including Tel Aviv, Paris and Exeter.
Everett, who has recently spoken out against police raids on brothels in central London's Soho, said: "Prostitutes are the world's unacknowledged experts on our most intimate desires."
Brand has spoken openly in the past about being treated for sex addiction and his encounters with prostitutes and wrote about it in his memoir, My Booky Wook.
Sara Ramsden, a commissioning editor at Channel 4, said: "Rupert has a unique authorial voice and his opinions range from the theological to the idealogical. It's great to see someone stand up so strongly for the dignity of women living with very difficult choices."
The programme is part of a raft of new shows announced by the channel including 24 Hours in Custody, which is filmed inside a Luton police station, a documentary about a group of Royal Marines new recruits and My Last Summer which follows the lives of five terminally-ill people and their families.