The team announced the news on Friday.
The deal is worth $1.55 million, a source told ESPN.com's Pierre LeBrun.
Morrow had 13 goals and 25 points in 71 games with St. Louis last season. In 921 NHL games with the Blues, Dallas and Pittsburgh, the 35-year old has 262 goals and 567 points.
Tampa Bay also signed forwards Philippe Paradis and Richard Panik to one-year, two-way contracts.
Panik had three goals and 13 points in 50 games with Tampa Bay last season, while Paradis played with Syracuse of the American Hockey League.
The Associated Press contributed to this report.