The 27-year-old Flutey, who can play fly-half or centre, has amassed almost 300 points for Irish in 36 appearances.
Wasps rugby director Ian McGeechan said: "We are very excited about signing Riki for next season.
"He is a quality player with ambition to win things, and he will add to the potential of our midfield and help take us forward in what we are trying to do to take the club forward."
Erinle, meanwhile, has been a rumoured target for Leicester, although it currently remains to be seen where he will play his rugby next term.
McGeechan added: "Ayoola is a talented player who has put in some fine performances for Wasps in his five seasons with the club. We wish him well in the future."