Brooksby, 30, has spent the past two seasons with the Seadogs and turned out in an unfamiliar left-back role for much of last season.
He becomes the fourth departure from the Flamingo Land Stadium in a week, after Tommy Taylor, James Walshaw and Chris Dawson all left for Buxton last week.
Manager Darren Kelly told the club’s official website: "Wayne is a great lad, he's somebody that has been brilliant for this club.
"We just couldn't agree a deal on him staying, so sadly he'll be moving on.
"I've been speaking to two keepers and I'm also very interested in two lads, who are currently involved in the National League North play-offs.
"There is no rush at the moment though, we just have to be ready for when the new season finally gets underway."
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