Snodgrass - Norwich's player of the year last term - was expected to leave Carrow Road after the Norfolk outfit suffered relegation from the top flight last season.
And his exit has now been confirmed, although the fee paid by Hull remains undisclosed.
A statement on Norwich's official website read: "City can confirm that Robert Snodgrass has completed his move to Hull City.
"The winger joins the Premier League club for an undisclosed fee on a three-year deal after two years with the Canaries."
A delighted Snodgrass, 26, told Hull's website: "Having spoken to the owners and the manager here, and having seen the plans they have for this club, I was very keen to be a part of it all.
"Once the fee was agreed between the two clubs, it all happened very quickly and everything the club has done to get the deal completed has been unbelievable.
"This is the start of an exciting new chapter for me and for my family and I just can't wait to get started now."
Snodgrass, a former Leeds United captain, moved to Norwich in 2012 and scored 14 goals in 74 appearances for the club.
The Scotland international is Hull's second significant signing of the close-season, joining midfielder Jake Livermore, who sealed his switch from Tottenham on Wednesday.
