The 21-year-old, who started his youth career at Wigan, was released by the Trotters at the end of last season having failed to make a first-team appearance, although he has gained experience of League Two football during loan stints at Southend and Accrington.
Boss Jim Bentley told the club's official website: "Jack has a good pedigree and has loads of potential.
"He's been at Wigan and Bolton and played in the league on loan at Southend and Accrington and I think he will have a lot to offer.
"He is still only young and we won't put too much pressure on him but I am really pleased that he has joined us. He has played for England (at Under-19 level) and comes highly recommended and I am sure he will make progress with us over the next two years."