"Dallas is such a great football player who elevated the horseshoe to another level when he came in," Colts owner Jim Irsay said.
Clark, 35, thanked quarterback Peyton Manning, saying, "Something about that man showed you how the game was supposed to be played, (the) importance of being accountable."
Clark then looked over at Wayne, paused, got choked up, pointed and said, "Thank you so much ... I was hanging onto your coattails."
Clark, the 24th overall pick by the Colts in 2003, set franchise records for receptions (427) and receiving touchdowns (46) by a tight end. He had the highest receiving yards of any tight end in postseason history when he had 317 yards in the 2006 playoffs, the year the Colts won Super Bowl XLI.
Clark was a salary cap casualty after the 2011 season.
"I'm a Colt, and I'm very lucky to say that," Clark said. "There's not 31 other teams like this. This is special."