The 31-year-old only joined Tranmere this summer, having been brought to Prenton Park by Ronnie Moore.
But following Moore's dismissal as manager, Allott has been told he does not figure in Barnes' plans.
Allott, a Spireites player between 2002 and 2007, has put pen to paper on a two-year deal at Saltergate to link up with Sheridan for a second time having worked with him at Oldham.
Barnes said: "Mark has been a pleasure to work with in my time at Tranmere.
"However, the opportunity for him to work with his former manager John Sheridan arose along with first team football - something I couldn't guarantee at Tranmere - so we have allowed him to move to Chesterfield.
"I'd like to wish him the best of luck for the rest of his career."