The 33-year-old ended last season with National League outfit Southend United, his second stint with the Shrimpers.
Manager Cox told bufc.co.uk: "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.
"He is an intelligent footballer, who is not only technically excellent, but also brings an experienced mindset into our midfield."
Atkinson follows Ben Pollock, Lebrun Mbeka, Ellis Myles, Jordon Crawford, Alex Brown and Scott Pollock into the Jakemans Community Stadium this summer.