The 26-year-old helped the Spireites reach the National League play-offs last season.
He rejoined Chesterfield for a second spell last December, having first played for the club in 2017.
Having began his career at Leicester City, McCourt has also featured for Port Vale, Northampton Town and Barnsley, among others.
Now he will play his football at Step 3 as Rylands look to continue their upward
“Jak came in to train with us short-term when Macclesfield Town were wound up,” said Blues manager Dave McNabb.
“He impressed immensely and we’ve kept in contact ever since. He’s a top class player who will bring real quality to the group.”
Photo credit: Warrington Rylands
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