Jets Coach Rex Ryan said he informed Sparano of the decision Monday.
Last week the Jets fired General Manager Mike Tannenbaum but said Ryan would be returning for the 2013 season.
Sparano was the team's offensive coordinator for one year after four years as the head coach of the Miami Dolphins. The Jets were 30th in the NFL in yards per game and 28th in points in 2012. They were 30th in passing yards and 12th in rushing.
The Jets were 6-10 in 2012 and will have the ninth overall selection in the 2013 NFL draft.
Celebrity Families of 2014 [PHOTOS]