Greene, 37, played in parts of 11 Major League seasons with the Angels, Blue Jays, Yankees Rangers, Rockies and Giants, compiling a .252 career average with 71 home runs and 217 RBIs while playing catcher, first base, outfield and designated hitter.
Greene also holds the distinction as the record holder for the most career home runs by a player with more home runs than walks (71 home runs, 67 walks). Bill Schroeder previously held the record (61 homers, 58 free passes).
Greene spent last season as a professional scout for the Padres after finishing his playing career in 2007 in San Diego's organization.
Tim Bogar held the quality assurance post for the Rays in 2008 before the Red Sox hired him during the offseason to become the team's first-base coach.
Duties for the position -- which was new in 2008 -- are likely to continue evolving under Greene, who will be in uniform during Spring Training and all regular-season pregame practices. In addition, he will assist with catching instruction, serve as a liaison between the scouting department and the club -- including series preparation and the coordination of Spring Training.
"It's kind of a hybrid job from the scouting thing I did this past season with the Padres," Greene said. "Obviously, being back on the field was definitely appealing to me."
Greene and Rays manager Joe Maddon have a relationship dating back to their days in the Angels' organization, which factored into Greene taking the job.
"If it wasn't with Joe and coming to a quality organization like Tampa has become, I probably wouldn't have left the Padres," Greene said. "But I thought this was a good opportunity for me to work with Joe, who I have a lot of admiration for from our years at Anaheim. And then to see what they've been able to do on the field and throughout the whole organization is pretty impressive.
"To me, the hardest thing to do in sports is to change a losing culture, and to me, the people who are in there running the organization now have done that."
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.