Jay O'Shea has left Bramall Lane after turning down the offer of a new two-year contract.
The attacking player spent the second half of last season on loan from Chesterfield and scored three goals.
He is out of contract at Chesterfield was offered a deal by Chris Wilder.
The United chief commented: "We offered Jay a good two-year deal but he has exercised his right to turn it down and look elsewhere. We thank him for his contribution in the second half of the season and wish him all the best for the future."