Boyes scored twice in 10 league starts for the Minstermen side last season, and has become United's fourth signing of the week.
The strengthening began on Monday with the signing of two midfielders: Josh Wright and Michael O'Connor.
That was followed by the arrival of centre-back Rob Jones from the Scottish Premier League side Hibernian on Thursday and Boyes on Friday.
Nigel Adkins, the Iron manager, described him as an impressive prospect.
"He's a player we think we can develop, he's one for the future and we've tracked him for a while," he told the official website.
"We're very pleased to bring another young and hungry player into the building."