Peterson, selected out of North Carolina Central, played primarily defensive end in college, but is expected to compete at defensive tackle.
Hayward, out of Portland State, is a linebacker who will compete at both outside positions, as well as for time at special teams.
Six more rookies remain unsigned with almost a week left before players must report to Orlando for training camp on July 26 — defensive end Gaines Adams, guard Arron Sears, safety Sabby Piscitelli, linebacker Quincy Black, tackle Chris Denman and running back Kenneth Darby.
Matthew Postins covers the Buccaneers for BucsBlitz.com and the Charlotte Sun-Herald in Port Charlotte, Fla. He is a member of the Pro Football Writers Association. Included among his more than two dozen writing and editing awards are national awards from the PFWA, the National Newspaper Association and the Associated Press Sports Editors, and state awards from the Florida Press Club and the Florida Sports Writers Association, for his coverage of the Buccaneers since 2004.