He enjoyed a brief spell back with the Tigers in 2016/17, joining on loan from Bolton Wanderers and scoring once in five appearances.
White has also featured for Glossop North End and most recently Bamber Bridge.
He made 11 appearances for the Brig last season, helping them to sixth in the Pitching In NPL Premier Division last season.
Commenting on his capture, manager Nick Spooner said: ”Ryan is another player who can play numerous positions. I’ve known him since he was a young lad at Bolton, he can play anywhere down the left and also in the 10 role.
“He knows the league and somebody who will make us stronger.”
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