Murray, 19, worked under McIntyre at Chester, where he remains as head of academy, and made 20 appearances for the first team.
Last season he had spells on loan in the Northern Premier League with Warrington Town and Atherton Collieries.
He becomes the second young Welshman to join the Linnets in recent days, following the capture of Jacques Welsh from Flint Town United.
Strikers Craig Lindfield and Kurt Sherlock have also agreed to stay with the club, while Linnets have signed another striker, Ryan Brooke from Mossley.
Brooke, 29, became McIntyre’s first new signing last week and scored against the Linnets for Mossley last season.
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