Clayborn, selected 20th overall from the University of Iowa, becomes the first No. 1 pick to reach a deal under the rookie salary system that's part of the new collective bargaining agreement. Clayborn's deal is for four years with a fifth-year option.
Clayborn is known as more of a run stuffer than a pass rusher, though he did have 11 sacks in 2009 for the Hawkeyes.
The Bucs also are working on a deal with second-round pick Da'Quan Bowers, who led the nation in 2010 with 16 sacks for Clemson, according to the Times.
In addition, the Bucs also came to terms with third-round pick Mason Foster, a linebacker from Washington, and seventh-rounder Daniel Hardy, a tight end from Iowa.
General manager Mark Dominik said Tuesday that it's a priority for the Bucs to sign their draft picks as quickly as possible.
"We're going to try and continue to push signing our draft picks quickly because I'd like to have every one of them out there the first day of training camp," Dominik said Tuesday. "And every day I can get them back here with our coaches and give them an opportunity to try to catch up as much as they can is really important to me."