Lea, 20, has spent pre-season at Glanford Park and played in friendlies against Brigg Town and Doncaster Rovers.
He was a free agent having been released by Manchester United, where he came through the youth setup, in the summer.
Scunthorpe have the option of extending Lea's deal by a further year next summer should they wish.
Lea is the fourth new arrival at Glanford Park this summer, following the defender Kenny Milne, winger Garry Thompson and striker Gary Hooper.