Martin went 16-4 with a 2.75 ERA in 160 1/3 innings (27 starts) for Triple-A Durham this season, and was named the International League's Most Valuable Pitcher.
"Any time you're throwing well, you're hopeful to get that opportunity," Martin said. "I just waited it out, and fortunately, something happened. It's nice to be here."
The 30-year-old has made 24 Major League starts, all for Washington in 2009 and 2010, going 6-9 with a 4.32 ERA. The 35th overall pick in the 2001 First-Year Player Draft has gone 88-53 with a 3.64 ERA over 13 Minor League seasons in the Indians, Nationals, Marlins and Rays organizations.
Given Martin's experience as a starter, manager Joe Maddon foresees using him in multiple-inning scenarios.
"We just wanted to make sure we're protected all the way around," Maddon said. "We've used our bullpen a lot. The part that scared us the most would be a lengthy situation. We thought it would be wise to have him here."
The Rays cleared a spot on the 40-man roster on Saturday by trading left-hander Frank De Los Santos to the White Sox for cash or a player to be named.
Adam Berry is a reporter for MLB.com. Follow him on Twitter at @adamdberry. Sam Strong is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.