Corbett, who was signed by Crewe as a youngster, has also been with Nantwich Town and is one of the players Ash Hoskin immediately targeted when he took over as manager.
“Zac has been in talks with other clubs, but has decided to come to us and I am delighted because he is final piece in the jigsaw.
“We wanted two wide men either side of the pitch, and now we have got them with Zac on the left and Robbie Booth on the right.
“Every target we have gone for we have now got and it is good to get all our business done early, before training starts, so we hit the ground running and are not scratching around for players at the end of July which I believe is what has happened in the past.
“I was determined that would not happen this year and I believe we have got together a very competitive squad with strong competition for places.”
The few remaining places in the squad will be filled from players who come along and impress in pre-season training.
Meanwhile Wes Baynes, who re-signed for the club this week, will be the new team captain.
“He is a leader and a popular figure in the dressing room,” explained the manager.