Jones, 27, came through the ranks at Bury and has had spells with Barnsley, Tranmere, Gateshead and Southport.
A club statement said: "This has been a very difficult decision for him after agreeing to re-sign for Stafford but he cannot turn down the opportunity to play back at a higher level.
"Andrai leaves with our best wishes and will always be welcome back at the Boro."
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