Both teams announced the deal in separate releases Tuesday afternoon. New England coach Bill Belichick released a statement that referred to Mankins as "one of the all-time great Patriots."
"Logan Mankins is everything we would ever want in a football player," Belichick said in the statement. "It is hard to imagine a better player at his position, a tougher competitor or a person to represent our program. He is one of the all-time great Patriots and the best guard I ever coached.
"Logan brought a quiet but unmistakable presence and leadership that will be impossible to duplicate. Unfortunately, this is the time of year when difficult decisions have to be made -- and this is one of the most difficult we will ever make -- but like every other decision, it was made for what we feel is in the best interests of the team."
A first-round draft selection in 2005, Mankins has spent his entire nine-year career with the Patriots and been New England's most consistent offensive lineman in front of star quarterback Tom Brady.
The 32-year-old Mankins should provide immediate stability to the Buccaneers' shaky offensive line, which has been short-handed at guard following Tampa Bay's injury settlement with veteran Carl Nicks.
"We feel very fortunate," said Buccaneers general manager Jason Licht, who previously spent three years in the Patriots' front office. "Logan is a very good player. [I'm] a firsthand witness of what he means to the locker room as well. I was with him for three years.
"Our director of player personnel, Jon Robinson, has been with him his entire career. His play on the field speaks for itself. He's a great person. He's going to be great for that room. He's going to be great for that locker room."
Mankins' primary position with the Patriots had been at left guard -- where Oniel Cousins, primarily a bench player in his six-year career, is slated to start for the Buccaneers. Tampa Bay also has been unsettled at right guard, where Patrick Omameh, who has never appeared in a regular-season game, has been the front-runner to start.
In an attempt to potentially improve their depth at the position, the Buccaneers hosted former Miami Dolphins guard Richie Incognito for a visit Monday. It marked Incognito's first trip to any NFL facility since his implication in the bullying scandal involving former Dolphins teammate Jonathan Martin.
"We always are going to leave options open of players that we think can be good fits and also be good players for us," Licht said. "So I wouldn't put an end to [signing Incognito]. That's just one of several options that are out there right now."
The Patriots and Mankins had a prolonged contract dispute in 2010, when he was a restricted free agent despite entering his sixth NFL season -- a result of a season without a salary cap changing the eligibility rules for restricted free agents.
Mankins didn't report to the team until the seventh week of the 2010 season, and it wasn't until the following offseason that the sides agreed to a six-year, $51 million contract extension.
The Patriots will save $6.25 million in cash this year and $7 million next year by trading Mankins. The trade also creates $5.755 million in cap space for New England in 2014.
Mankins was a captain the past three seasons for the Patriots. His departure creates an opening for second-year guard Josh Kline to potentially elevate to a starting role. Kline started at left guard Dec. 22 against the Baltimore Ravens when Mankins was forced to move to left tackle.
The Patriots have struggled to fill their tight end depth chart behind Rob Gronkowski, who has missed 14 games over the past two seasons because of injuries. Since Aug. 10, the team has made 10 transactions at the position.
The 6-foot-4, 220-pound Wright, who is more of a pass-catcher than on-the-line blocker, would supplement the position and potentially create a one-two combination similar to what the Patriots had with Gronkowski and Aaron Hernandez from 2010 to 2012. The Patriots also have five-year veteran Michael Hoomanawanui who is likely to stick on the roster this year.
Wright played at Rutgers under former Bucs coach Greg Schiano, who remains a close friend of Belichick. A few weeks ago in training camp, Schiano was a guest of Belichick's at practice.
ESPN.com Buccaneers reporter Pat Yasinskas, ESPNBoston.com's Field Yates and Mike Reiss contributed to this report.