He links up with former Kidsgrove boss Ryan Austin.
Duffy, 34, joined Kidsgrove last summer after being released by Notts County, having previously played for Swansea City, Burnley, Coventry and Port Vale.
Boss Scott Dundas said: “I don't know Richard but we wish him and Ryan (Austin) all the best at Congleton
“It is a great club, I played for them myself in the 2008/09 season when Anthony Buckle was the manger. So we wish them all the best and I hope they have a good season."
Duffy made 35 appearances for Kidsgrove, scoring once in an FA Trophy win over Daventry Town.
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