The 29-year-old winger made 13 appearances for the Dabbers, scoring three goals.
A former Blackpool, Accrington Stanley and Shrewsbury Town player, he joins Bamber Bridge who currently sit in fourth place in the Northern Premier League.
On his move, Caton said: "I'm delighted to join Bamber Bridge. The lads are flying and I am excited to be a part of the promotion push.
"Thanks to Jamie Milligan and John Hills for bringing me on board for what is going to be a great end to the season."
He will go into contention for Brig's next game away at Atherton Collieries in the Lancashire Trophy semi-final on Wednesday night, before facing his former club Nantwich Town in league action on Saturday.
Photo credit: Bamber Bridge
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