On November 5, 2015, Morrison, Brad Miller, and Danny Farquhar were traded to the Tampa Bay Rays in exchange for Nathan Karns, C. J. Riefenhauser, and Boog Powell.

Morrison would wear number 7 during his time with the Rays.
Having supplanted incumbent first baseman James Loney with a solid spring training, Morrison began 2016 with the lion's share of starts at first base, with utility man Steve Pearce as his platoon-mate.
He appeared in 107 games in his first season in Tampa Bay, making 78 starts at first base, and 17 as designated hitter.
For the 2016 season he hit .238/.319/.414 with 14 home runs and 43 RBIs in 353 at bats, striking out in a career-high 22.4% of his plate appearances.
Morrison played his final game of the season on September 11, as a torn left wrist sheath injury requiring surgery cut his season short.
Of the 95 starts he made, only 11 came against left-handed pitchers, and as a whole, Morrison hit .258 (16-62) against lefties while benefiting from a .341 BAbip, compared to his overall BAbip of .278.
 After the 2016 season, he became a free agent.
On February 6, 2017, Morrison signed a one-year contract worth $2.5 million to remain with the Rays for the 2017 season.

Morrison showed improved power and situational hitting in 2017, becoming the everyday first baseman, instead of the original plan of platooning with right-handed hitter Rickie Weeks Jr. On May 22, Morrison hit his 12th home run of the year; on that day in the 2016 season, Morrison hit his first of the year.
On May 31, he hit his 15th home run of the year, passing his 2016 total of 14.
On July 1, Morrison hit his 23rd and 24th home runs against Dylan Bundy, passing his career high.
After being snubbed by the Home Run Derby and missing out on the All-Star vote, Morrison was left out of the All-Star festivities in 2017.
He voiced his displeasure with the Home Run Derby selections by criticizing Gary Sánchez, who had 13 home runs and was the final player allowed in the derby, saying, "I remember when I had 14 home runs ... that was a month and a half ago".
Morrison became only the second player in history with 24 or more home runs at the All-Star Break not to be selected.
In 2017 he batted .246/.353/.516 with 85 RBIs and was 4th in the American League in intentional walks (with 8), 5th in home runs (38; a career high, and 3rd-most in club history), 6th in at bats per home run (13.5), and 8th in walks (81) in 512 at bats, while playing first base.
He hit a home run every 9.67 at bats in games on the road, the 9th-best rate in American League history.
On November 5, 2015, Morrison, Brad Miller, and Danny Farquhar were traded to the Tampa Bay Rays in exchange for Nathan Karns, C. J. Riefenhauser, and Boog Powell.
Morrison would wear number 7 during his time with the Rays. Having supplanted incumbent first baseman James Loney with a solid spring training, Morrison began 2016 with the lion's share of starts at first base, with utility man Steve Pearce as his platoon-mate. He appeared in 107 games in his first season in Tampa Bay, making 78 starts at first base, and 17 as designated hitter. For the 2016 season he hit .238/.319/.414 with 14 home runs and 43 RBIs in 353 at bats, striking out in a career-high 22.4% of his plate appearances. Morrison played his final game of the season on September 11, as a torn left wrist sheath injury requiring surgery cut his season short. Of the 95 starts he made, only 11 came against left-handed pitchers, and as a whole, Morrison hit .258 (16-62) against lefties while benefiting from a .341 BAbip, compared to his overall BAbip of .278.  After the 2016 season, he became a free agent. On February 6, 2017, Morrison signed a one-year contract worth $2.5 million to remain with the Rays for the 2017 season.
Morrison showed improved power and situational hitting in 2017, becoming the everyday first baseman, instead of the original plan of platooning with right-handed hitter Rickie Weeks Jr. On May 22, Morrison hit his 12th home run of the year; on that day in the 2016 season, Morrison hit his first of the year. On May 31, he hit his 15th home run of the year, passing his 2016 total of 14. On July 1, Morrison hit his 23rd and 24th home runs against Dylan Bundy, passing his career high. After being snubbed by the Home Run Derby and missing out on the All-Star vote, Morrison was left out of the All-Star festivities in 2017. He voiced his displeasure with the Home Run Derby selections by criticizing Gary Sánchez, who had 13 home runs and was the final player allowed in the derby, saying, "I remember when I had 14 home runs ... that was a month and a half ago". Morrison became only the second player in history with 24 or more home runs at the All-Star Break not to be selected. In 2017 he batted .246/.353/.516 with 85 RBIs and was 4th in the American League in intentional walks (with 8), 5th in home runs (38; a career high, and 3rd-most in club history), 6th in at bats per home run (13.5), and 8th in walks (81) in 512 at bats, while playing first base. He hit a home run every 9.67 at bats in games on the road, the 9th-best rate in American League history.
Logan Morrison