Hovan, 31, is a 10-year veteran, coming off his fifth season with the Buccaneers. He was scheduled to make $4 million for the 2010 season.
Jevan Snead, the starting quarterback the past two seasons for Mississippi, led a group of 12 undrafted free-agent rookies the Buccaneers have signed. Snead threw for 2,762 yards with 26 touchdowns and 13 interceptions for the Rebels in 2009.
The 25th overall selection in the 2000 draft, Hovan was an immediate starter for the Minnesota Vikings and played at a high level for the first three seasons of his career.
But his production slipped, he fell out of favor with the Minnesota coaching staff his final two years with the club and his playing time was reduced.
He signed with the Buccaneers in 2005 and made an immediate impact on the team's run defense. He signed a five-year, $17.5 million extension in 2006.
After netting 11 1/2 sacks combined in 2001-02, Hovan totaled just 3½ the following two seasons and has only five in five seasons since.
Sears was a second-round draft pick in 2007. He started 31 games in his first two seasons with the team, but sat out all of last season on the non-football illness list. The Bucs have not publicly discussed the reason.
Askew spent much of last season on the non-football injury list after being involved in a car accident.
Information from ESPN.com senior writer Len Pasquarelli and The Associated Press was used in this report.