The 23-year-old right-back, who completed a free transfer from Oldham on Monday, is the Owls' second summer signing after winning automatic promotion to the Championship following the arrival of goalkeeper Chris Kirkland from Wigan.
Lee, a product of Manchester United's academy, told Wednesday's official website: "I've learned a lot in my time at Oldham and would like to thank the club for everything they have done for me.
"But when a chance like this comes along you have to take it. Every player wants to play in front of the biggest crowds possible and I've seen myself what kind of support this club gets week in, week out so it's really exciting.
"I think Sheffield Wednesday can reach the Premier League and that's definitely what you've got to aim for."