The Tipperary man had been recommended for the role by a working group chaired by former Tipperary manager Liam Sheedy.
Kelly had been in charge of Kerry for the past two seasons, leading them to Christy Ring Cup success this year, as well as promotion to Division 1B.
He has also managed his own club, Kildangan, to an All-Ireland Intermediate title in 2005 and has been involved with various Tipperary teams, as well as the Fitzgibbon Cup team at the University of Limerick.
Kelly replaces Brian Whelehan in the role after the former All-Ireland winner stepped down this summer.
He is the fourth Tipperary man to take over the reigns of Offaly hurling.
