The 30-year-old agreed personal terms on Tuesday before successfully completing his medical at the club’s Thorp Arch training ground.
Hunt scored 39 goals in 162 appearances during his five-year stay at the Madejski Stadium, where he previously played under Whites manager Brian McDermott.
"Noel is a player that I scouted five years ago when he was playing for Dundee United," McDermott told the club’s official website.
"We spent £500,000 on him at the time, and that was money very well spent. He's an infectious character and I'm sure he will engage Leeds United fans with his desire and determination, and never say die attitude.
"He will bring an awful lot to our squad on and off the pitch, and I'm delighted he's chosen to come and play for Leeds."
Hunt was an integral part of McDermott’s promotion winning side in 2011, but struggled to make an impact in the Premier League as the Royals made an immediate return to the Championship after finishing 19th.
The Waterford-born frontman, who has three Republic of Ireland caps to his name, becomes Leed’s third signing of the close season after striker Matt Smith and midfielder Luke Murphy joined from Oldham and Crewe respectively.
Hunt could make his Leeds debut in Saturday’s pre-season friendly opener against Farsley.