Arsenio and Sinead tell TMZ, in a joint statement, "Sinead has retracted and apologized for statements she made about Arsenio last year, which prompted his defamation lawsuit against her."
TMZ broke the story ... Arsenio sued the crap out of the singer after she went on a rant -- weeks after Prince's death -- and accused him of fueling Prince's drug habit.
Sinead tells us, "I apologize for my Facebook posts about Arsenio to the extent that anyone thought I was accusing him of acting as Prince's drug dealer and supplying him with illegal hard drugs, or insinuating that Arsenio had something to do with Prince's death. I sincerely apologize because those statements would be false, and I retract them unequivocally."
Arsenio isn't spiking the football in victory -- his reps say he'll file to dismiss the lawsuit, now that Sinead's admitting she was wrong.