Simms' older brother, Chris Simms, played in the NFL, too.
"I just want to keep playing football," Matt Simms told New York reporters. "It's as simple as that. I just want to keep playing the game that I've been playing since I was a child."
The Jets now have five quarterbacks on the roster: Mark Sanchez, Tim Tebow, Greg McElroy, G.J. Kinne and Simms.
The Jets also signed sixth-round safety Josh Bush and offensive lineman Fredrick Koloto, cutting center Kris O'Dowd.
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