Snodgrass has signed a three-year deal after the clubs agreed an undisclosed fee, believed to exceed £6m.
"We are delighted to confirm Robert Snodgrass as our second major signing of the summer," Hull said in a statement.
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
The deal for Snodgrass, 26, comes just days after Hull paid a club-record fee for midfielder Jake Livermore.
"Having spoken to the owners and the manager, and seen the plans they have for this club, I was very keen to be a part of it all," said Snodgrass.
"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 can't wait to get started."
Snodgrass, who joined Norwich from Leeds United in 2012, scored seven goals in 34 appearances last season as the Canaries were relegated from the Premier League.
Snodgrass will meet up with his new team-mates for the first time when the squad returns for pre-season training next week.
Livermore, 24, joined the Tigers from Tottenham last Wednesday for a fee thought to be about £8m.
Steve Bruce's Hull, who begin their debut Europa League campaign on 31 July, face promoted Queens Park Rangers in their first match of the new Premier League season on 16 August.
Hull City have completed the signing of Scotland midfielder Robert Snodgrass from Norwich City.