The team claimed him off waivers Friday, one day after he was released by New England.
Wright (6-foot-4, 220 pounds) entered the NFL as a college free agent out of Rutgers in 2013. He had 54 receptions for 571 yards as a rookie and scored five touchdowns.
Last season for New England, as a backup to All-Pro Rob Gronkowski, Wright made 26 catches for 259 yards, and scored six times.
To make room for Wright, the Bucs waived tight end Taylor Sloat.