The hiring was announced Wednesday by head coach Dennis Allen.
Sparano, who was fired as the Jets' offensive coordinator after one season, had earlier interviewed to become the Kansas City Chiefs' offensive line coach. Andy Reid had said the interview went well, but he ultimately hired Andy Heck for the position.
Sparano has been in talks with several teams for offensive line coaching jobs since he was fired by the Jets. He was set to visit with the Browns earlier this month, but George Warhop decided to stay in that same job with Cleveland.
The Jets were ranked 30th in total offense in Sparano's first and only season in the role, doomed by their unsettled quarterback position.
Sparano also was unable to determine a role for Tim Tebow, who didn't have much of an impact after he was acquired in a trade with the Broncos. New York's Wildcat package was ineffective, and the Jets were unsure how to use Tebow in other packages.
Sparano was the head coach of the Miami Dolphins before joining the Jets. In his almost four years as Miami's coach, Sparano went 29-32.
Information from ESPN NFL Insider Adam Schefter, ESPN senior NFL analyst Chris Mortensen and The Associated Press was used in this report.