The Dane, who played in the Premier League with West Bromwich Albion and Burnley, was a free agent following his release by Bury at the end of last season.
Speaking to the club's official website, the 38-year-old said: "I'm really excited about this new challenge at this stage of my career. I still feel I have a lot to offer. I had a really good season at Bury but the opportunity to move to an ambitious League One club and work with an experienced manager like John Gregory was too good to turn down."
Meanwhile, manager Gregory added: "I'm delighted to have Brian at the club. He's still a superb goalkeeper who is in fantastic physical condition. He is a real presence in the penalty areas and a character who will be great in the dressing room and around the club.
"As usual, we have done a lot of research into our signings and I have spoken to a lot of managers and people in the game about Brian and without exception they have all spoken very highly of him."
The Reds will be the seventh club that Jensen has represented.