The 22-year-old defender has spent the last two years with the Pirates but injury restricted him to 22 games during a frustrating 2008/09 campaign.
He admitted the time was right for a new challenge as his contract had expired.
Jacobson told the Oldham Chronicle: "I think I have joined a bigger and better club than Bristol Rovers and I am delighted to have the opportunity to play here.
"I am looking for us to be up near the top challenging for promotion. I cannot wait to get started."