Egan, 20, turned out for the Colls in a number of pre-season games, including against Altrincham.
He came through the ranks at Carlisle United, making his debut in the EFL Trophy, as well as having spells at Workington and Clitheroe, before moving to Witton in March.
Manager Michael Clegg said: “Jack has been a big hit with all the staff and the players during pre-season. He has had a little injury and this is why we haven’t seen so much of him, but on the training ground he has been fantastic.”
Meanwhile, Colls have confirmed that Marcus Perry has returned to former club Irlam.
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