The story was confirmed by ESPN's Michael Smith, a good friend of Jets coach Eric Mangini.
While the draft pick couldn't be confirmed on Wednesday night, it has been speculated that the Jets sent a third or fourth round pick that could turn into a higher pick based on the performance of Favre and the Jets in 2008.
It's unclear what the Jets will do with Chad Pennington, but he will likely be traded or released.
"I am looking forward to seeing Brett Favre in a New York Jets uniform," said Jets Chairman & CEO Woody Johnson. "He represents a significant addition to this franchise."