Smith, 27, had 129 catches for 1,252 yards and 11 touchdowns in four seasons with Tampa Bay. He was traded in the offseason to the New England Patriots, who released him Saturday.
Smith will back up Brent Celek, who emerged as the starter late last season, replacing the now-departed L.J. Smith.
A four-year player at Stanford, Smith was the runner-up to current Pittsburgh Steelers player Heath Miller for the 2004 Mackey Award, given annually to the nation's top college tight end.