The team announced left-handed pitcher John Gaub was designated for assignment to make room on the 40-man roster for Sutton.
"It was a very wide range of emotions in about four hours," Sutton said. "There was a lot of different phone calls."
He added that his roommate on the road was former Rays player Josh Wilson, who assured Sutton he was going to a good situation.
"He said it's an awesome place to be," Sutton said. "Great staff, great clubhouse, great guys -- it's just a great place to play."
Sutton, 28, was hitting .270 in 38 games for Triple-A Gwinnett. He has played in 86 Major League games for the Reds, Indians and Red Sox, batting .258 with 24 RBIs in 159 at-bats. He signed a Minor League deal with the Braves last offseason after hitting .315 for Boston in limited time.
He played mostly second base for Gwinnett, appearing in 30 games there, seven at third base and one at first.
Sutton already has connections to many of the Rays' players, including utility man Ben Zobrist. The two were drafted together by the Houston Astros in 2004, and Sutton said Zobrist is already helping him settle in.
"That's just an added bonus that he's here," Sutton. "Just going over scouting reports, he's kinda explained how everything goes around. It's gonna be a big help."