Sparano, whose father served as the Jets' offensive coordinator in 2012, spent the last two seasons with New York as a seasonal intern. The former University of Albany defensive end was an assistant defensive line coach with the UFL's Hartford Colonials in 2010, and served as an offensive quality control coach with the Miami Dolphins in 2011.
Smith was a third-round pick of the Jets in 2006, and played all seven of his NFL seasons with New York. He had six interceptions and 3 1/2 sacks while also playing a key role on the Jets' special teams unit.
The Jets announced the moves on Monday.
AP NFL website: www.pro32.ap.org