The 33-year-old ended last season with National League outfit Southend United, his second stint with the Shrimpers.
Cox said: “We are delighted to have completed the signing of Will.
“Understandably, he was much sought after following his time at Southend and we are delighted to have him onboard.
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“He is an intelligent footballer, who is not only technically excellent, but also brings an experienced mindset into our midfield.
Atkinson, who has also played for several other clubs including Hull City, Bradford City, Port Vale and Alfreton Town, had two spells with the Stags.
The first was as a youngster on a two-month loan from Hull under Billy Dearden in 2008.
He was then Steve Evans' 11th summer signing for the Stags in 2017.
David Flitcroft replaced Evans and transfer-listed Atkinson at the end of the season only to change his mind and keep him as a squad member, mostly on the bench.
Flitcroft was himself gone the next summer and new boss John Dempster released Atkinson in May 2019.