The trade was completed just prior to the 16:00 Eastern Time deadline but no details were given about what New England was sending to Tampa Bay.
Talib, who has also had off field run-ins with the law, is currently serving a four-game suspension for violating the league's policy on the use of performance-enhancing drugs.
The 26-year-old corner was also suspended for the Buccaneers 2010 season-opener for violating the NFL's personal-conduct policy.
Taken in the first round of the 2008 draft by the Buccaneers, Talib has developed into one of the league's premier defenders, recording 18 interceptions over five seasons while returning three for touchdowns, including two last season.
Talib's addition should help bolster a leaky Patriots pass defense that ranks near the bottom of the league, surrendering 281 yards a game.
The trade deadline had been pushed back from Tuesday to Thursday because of Hurricane Sandy but the delay produced little beyond some intriguing rumours.
As the deadline approached, there had been talk that the St.
Louis Rams were entertaining offers for Pro Bowl running back Steven Jackson while the Carolina Panthers were considering shopping running back DeAngelo Williams.