The team announced the deal with the unrestricted free agent on Monday.
Tampa Bay coach Raheem Morris said Hayward was probably the Bucs' special teams MVP last year.
In four seasons with the Buccaneers, Hayward has 58 kick-coverage tackles, including a team-best 20 in 2010.
To make room for Hayward on the 90-man training camp roster, the Buccaneers released rookie running back Deonte Jackson.
Also, Tampa Bay worked out in pads for the first time at training camp during its Monday afternoon practice.
"The first day of pads is always a fun one," quarterback Josh Freeman said. "You've got a lot of energy, a lot of passion."
Both candidates for the starting offensive right tackle spot, Jeremy Trueblood and James Lee, are among the players not allowed to practice yet because of the new collective bargaining agreement reached last week.
"It is strange," Morris said. "But it's fine. Everybody is going to start at the same time. We'll have two guys competing to start once they get an opportunity to get out there on the field."
Once the CBA is fully squared away, veteran free agents who have signed new contracts recently will be allowed to practice with their teams. Those players are currently allowed to attend team meetings, work out individually and watch — but not participate — in practice.