In return, New England will ship a late-round 2015 draft pick to St. Louis for Salas, who was a fourth-round pick of the Rams in 2011.
Salas (6 feet 1, 209 pounds) played in six games last season, catching 27 passes for 264 yards, while also fumbling three times. His season was cut short by a broken fibula suffered on Nov. 6 against the Cardinals.
The Rams' offensive coordinator for Salas' rookie season was Josh McDaniels, who rejoined the Patriots in January.
The 24-year-old was a three-year starter at Hawaii, where he was named an Associated Press third-team All-American in 2010.
Salas adds to a thin wide receiving corps in New England. The Patriots made the surprise move by cutting 11-year veteran Deion Branch on Friday.
It looked like the 33-year-old Branch had outlasted the field to earn a spot as a No. 3 receiver behind Wes Welker and Brandon Lloyd, especially given his knowledge of the team's system and his rapport with quarterback Tom Brady.
New England also cut ties with linebacker Bobby Carpenter.
Tennant, who enters his third NFL season, has appeared in 28 regular-season games over the past two years (no starts). He was selected by the Saints in the fifth round of the 2010 draft.
Longtime center Dan Koppen, who had been with the team since 2003, was released Friday.
Mike Rodak is a contributor to ESPNBoston.com. ESPNBoston.com's Mike Reiss contributed to this report.