The winger was entering the final year of his contract at Carrow Road and will now stay in the Premier League after penning a three-year deal with the Europa League debutants
The 26-year-old becomes the FA Cup finalists' second new recruit of the summer after the club-record £8 million purchase of Jake Livermore from Tottenham.
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"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," he told the club's official website.
"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."
The Scotland international notched seven times from a wide position in 34 appearances but was entering the final year of his contract at Carrow Road.
Hull begin their first ever Europa League campaign on July 31.