Posada, 40, played 17 years in the major leagues, all with New York, helping the Yankees win the World Series in 1998, 1999, 2000 and 2009.
"Every time I stepped through the Yankees Stadium doors I quoted Joe DiMaggio, 'I want to thank the good Lord for making me a Yankee,'" he said during a Yankee Stadium news conference called to officially mark his departure.
"I was able to live my dream to play baseball for the best sports franchise ... the New York Yankees. Playing for the New York Yankees has been an honor. I could never play for another team. I will forever be a Yankee."
Hours later, the Yankees announced current catcher Martin had inked a one-year contract, thereby avoiding arbitration.
The 28-year-old hit .237 with 17 doubles, 18 home runs and 65 RBI over 125 games for New York last season, the first with the Yanks for the three-time all-star.