The defender, who had been on-loan at the Crown Ground, has signed a deal until the end of the season after he was released by Oldham.
Jacobson was delighted to secure the move on a permanent basis.
"I'm very pleased that it's all done," he told the club's official website.
"It's been a bit up in the air today about what was happening but I've managed to sign permanently until the end of the season.
"It's been good in the last few months playing games and doing well. I like the boys here and the way they play and the management and everything. It's good for me."