Thompson, born in Shrewsbury, was a product of the Town youth system before joining Fulham. He failed to make the breakthrough at Craven Cottage, and played a few games for Mansfield and Northampton.
He made only one appearance last term for Chesterfield, and was subsequently released. He had been training with Town and played 45 miutes in the win over Stoke, making several key saves.
This, and his performances in training, were enough to convince boss Gary Peters to hand Thompson a one-year deal.
Peters told ShrewsWeb that Thompson would come in as an understudy to teenage kepper Joe Hart: "Glyn's a good shot stopper, comes for crosses and his kicking is not too bad.
"If Glyn continues to work hard then he has every chance of playing, Joe Hart is only 18, and with youth comes inconsistency, so if Joe has a couple of bad games then we've now got Glyn to step in."