The 26-year-old contributed to over 70 goals in 178 appearances for the Seals, making him one of only three players to have made over 150 outings for the reformed National League North outfit.
He will add versatility across the Boro frontline and becomes their fifth summer signing as they look to re-build after narrowly missing out on a play-off spot last season.
As well as Chester, Dudley has also played for the likes of Macclesfield, Salford City and Bury, where he featured in a number of EFL games with the Shakers in both League One and League Two.
It is the third time he has worked with Radcliffe managerial duo Anthony Johnson and Bernard Morley, having played for them at both Salford and Chester.
Photo credit: Radcliffe
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