The 22-year-old former Middlesbrough forward's new side face Northampton at Sincil Bank on Tuesday 2 November.
Boss Chris Sutton told BBC Lincolnshire: "Ben will certainly score goals at this level. He is particularly quick and powerful.
"I am very excited about him coming. It is a major coup for the club that he has agreed to join us."
Celtic signed Hutchinson in January 2008 but he has struggled for first-team chances with the Glasgow giants.