Crystal has hosted the prestigious award show eight times, most recently in 2004.
"Am doing the Oscars so the young woman in the pharmacy will stop asking my name when I pick up my prescriptions. Looking forward to the show," Crystal tweeted.
Ratner resigned Tuesday, in the aftermath of the outcry over his use of a homophobic slur at a public screening for his film "Tower Heist," and Murphy stepped down Wednesday.
Brian Grazer was selected to serve as producer for the 84th annual Academy Awards ceremony, that will be held on February 26, 2012, at the Kodak Theatre in Hollywood, California.