The clubs agreed a fee for the 26-year-old on Thursday, understood to be a one-off payment of £7million, and personal terms have now been settled on the winger’s switch to the KC Stadium.
It is the second major signing of the close season for the Tigers, who last week bought former loanee Jake Livermore from Tottenham for a club record fee rising to £8million.
Like Livermore, Snodgrass fits manager Steve Bruce’s preferred profile of players with Premier League experience, a model he enjoyed success in Hull’s first season back in the top flight.
Snodgrass had a year left on his contract at Carrow Road but was eager to avoid dropping down a division following last season’s relegation.
Sunderland and Stoke had been linked with a move for the player, but are thought to have been put off by a price tag Hull were willing to meet.
He made 34 appearances in 2013-14, scoring seven times.
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Speaking after putting pen to paper on a three-year deal, Snodgrass told www.hullcitytigers.com: “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.”
Hull, who have the added commitment of Europa League football following their FA Cup final appearance in May, have also been linked with a move for Bristol Rovers teenager Alefe Santos.
The Conference side tweeted that the 19-year-old Brazil-born midfielder had turned down a new contract and mentioned Hull as a possible destination, but the Tigers are not understood to have made a formal offer to Santos.
“Alefe Santos has decided not to sign a new deal with Bristol Rovers. We understand that Santos is in talks with Hull City. Any fee for Santos will have to be determined by tribunal,” Rovers wrote.