The 19-year-old has penned an 18-month contract at Gresty Road having trained with the Alex squad for a large part of the season, making a number of reserve team appearances.
Guthrie leaves Wessex Division One side Pewsey Vale - who operate six levels below the Football League - having initially arrived in Cheshire in September last year on a short-term trial.
After impressing he was offered an extended trial that began in November and now becomes Steve Davis' first permanent signing since replacing Dario Gradi as manager last year.
"The lads have all made me really welcome and I feel settled in the squad," Guthrie told The Sentinel. "It has been a long process, but I'm delighted to have signed, even though it hasn't really sunk in yet. It is an amazing feeling."
"It has obviously been a big step up coming from the league I was playing in, and the reserve games against the likes of Bolton and Wolves were a real challenge. I also need to physically bulk up and then hopefully all of the hard work will pay-off and I'll be in and around the first team."
