The 40-year-old, who has made almost 600 appearances in his career, was released by the Spireites at the end of last season after two years at the club.
The former Nottingham Forest, Derby County, Reading, Wycombe and Doncaster Rovers forward had previously hinted that he may hang up his boots when he reached 40 but the forward now plans on continuing.
Tyson departs the Blues having written his name into the history books, becoming the first Chesterfield substitute to score a hat-trick.
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He has now signed for Northern Premier League East division side Grantham in Lincolnshire.
"The gaffer wants me to go out there and enjoy myself and pass on the experience that I have learnt over the last few years,” he said.
Tyson signed a new deal last summer but found his game time very limited and he had a short loan spell at Alfreton Town.
His last appearance for Chesterfield as a second-half substitute in the play-off win against Halifax in May.