Downing joins new OC Nathaniel Hackett, the erstwhile head coach of the Denver Broncos, and running game coordinator/offensive line coach Keith Carter in New York.
Downing was fired by the Titans on Jan. 9, two days after their season ended in a loss at Jacksonville. The Titans finished the season on a seven-game losing streak after starting 7-3. Three other coaches, including Carter, also were fired.
Downing reportedly served two days in jail late last month for a DUI arrest last November. Downing was arrested on charges of driving under the influence and speeding at 4 a.