The 23-year-old has put pen-to-paper at the Jakemans Community Stadium and could be in action for the first time when the Pilgrims entertain Doncaster Rovers on Tuesday evening.
Gyasi, who played under manager Ian Culverhouse at the Walks Stadium, had a year remaining at Chesterfield, but agreed a mutual termination ahead of his new challenge in Lincolnshire.
The Hamburg-born frontman will wear squad number 12.