The centre-back played 50 games in the National League North for Blyth across two spells.
Elsdon also has a National League winners medal in his locker after helping Barrow achieve promotion to the Football League in 2020.
Now the former Middlesbrough, Inverness and Clyde defender has become Daniel Moore’s fourth new signing ahead of the 2023/24 season.
“I'm absolutely buzzing to be here," Elsdon said.
"The gaffer has spoke to me for a while and I'm delighted to finally join the club.
"I can't wait to get started and hopefully have another run of games like last season."
Photo credit: Hebburn Town