Quinn made 28 Premier League appearances in the Tigers midfield last season but was unable to stop them dropping into the Sky Bet Championship on the final day of the campaign.
He has also won 13 senior caps for the Republic of Ireland and Reading boss Steve Clarke is delighted to have secured one of his main summer transfer targets.
His career started in Ireland with St Patrick’s Athletic, before he made a move to England with Sheffield United, where he made more than 200 appearances. Quinn joined Hull in 2012 for an undisclosed fee and was closing on a century of appearances before the expiry of his deal.
Clarke told the club’s website: “Stephen is an unassuming player but has always caught my eye and, when I knew he was available, I targeted him quite early in the summer.
“His performances are always of a good standard and he is a talented, industrious, aggressive midfielder who can be influential in games.
“Obviously he has just experienced relegation at Hull City and is desperate to get back to the Premier League as quickly as possible, which can only be good for us.
“He has previous experience of playing in the Championship and was an important member of the Hull City team that gained promotion in 2012/13 season.
“Stephen is also a good character who will have a positive effect in our changing room and, just as importantly, on our younger players here at Reading FC.”