Partridge, 26, was one three players told that they were free to leave Millmoor earlier this week, as Mark Robins and John Breckin continue with what is set to be one of the biggest close season overhauls that the club has ever seen.
Partridge is the second signing of the summer for Chester's manager, ex-Millers' favourite Bobby Williamson, the first being Nathan Lowndes, who had a largely undistinguished loan spell at Millmoor in 2002.