Stinnett signed a one-year deal for $650,000 to become Jorge Posada's understudy. The move is the second free agent signing of the offseason for the Yankees, who inked Hideki Matsui to a four-year deal in mid-November.
For Stinnett, the chance to get to the postseason was the biggest draw in signing with New York. The catcher, who will turn 36 before Spring Training, has been to the playoffs just once, in 1999 with Arizona.
"It's pretty exciting," Stinnett said. "To join the best team in all of baseball, it will be special to put the pinstripes on."
Flaherty had been Posada's backup for the past three seasons, appearing in 134 games for the Yankees. Flaherty hit .225 with 12 home runs and 41 RBIs in 359 at-bats, though his average was just .165 in 127 at-bats last season.
Flaherty served as Randy Johnson's personal catcher for the final four months of the 2005 campaign, as the big left-hander worked better with the backup than he did with Posada. But Johnson didn't fare well in his only postseason start with Flaherty, then pitched well in relief with Posada behind the plate.
Stinnett is also familiar with Johnson, having caught the left-hander in 1999-2000 with the Diamondbacks -- two of Johnson's five Cy Young seasons.
"He's a challenge to catch," Stinnett said. "It takes a lot to catch him, because he brings a lot to the table. He throws hard, he's intense, and he expects a lot out of his catcher."
Earlier this month, general manager Brian Cashman said that Flaherty's role as Johnson's catcher would not affect his decision on a backup catcher.
"I'm not really focused on who catches Randy," Cashman said. "I'm focused on filling a need for a backup catcher with the best candidate possible."
Stinnett spoke with manager Joe Torre on Tuesday, as the two chatted about Stinnett's philosophy on catching and working with a pitching staff. They didn't speak specifically about Johnson, but Stinnett feels that his familiarity with the Big Unit will help him with his new club.
"I told Joe, 'I know Jorge is the No. 1 guy,'" Stinnett said, "but my job is to come in and push him, try to get as much playing time as I can without upsetting the environment."
Stinnett underwent Tommy John surgery on his right elbow in June 2004, but the Yankees are confident that he is healthy after examining him.
Last season with Arizona, Stinnett hit .248 with six home runs and 12 RBIs in 59 games. In 12 seasons with the Mets, Brewers, Diamondbacks, Reds, Phillies and Royals, Stinnett is a .239 hitter with 63 homers and 216 RBIs.
Mark Feinsand is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.