The 30-year-old will play one of the outfield corners against right-handed pitchers and also get some time at designated hitter and backing up center fielder Kevin Kiermaier, the source said.
Rasmus was the Houston Astros‘ second-highest-paid player last season, making $8 million, but batted just .206 in 107 games while dealing with various injuries.
FanRag Sports earlier reported Rasmus’ deal with the Rays.
Rasmus hit .238 with a career-high 25 home runs and 61 RBIs in 2015, his first season with the then-AL wild-card champion Astros. He had four homers in six postseason games, including one in the AL wild-card matchup with the Yankees.