Murphy is understood to have undergone a medical, with the transfer is set to be confirmed within the next few days. Should the deal go through as expected, he will become Neil Warnock's first signing since being promoted back to the Premier League, as reported by the Telegraph.
The 23-year-old scored seven goals and assisted another three assists 41 league games, standing out in what was another relatively disappointing season for Norwich, with the Canaries finishing 14th under Daniel Farke.
Murphy has made a number of appearances in the England youth set-up in the past, finding the net for England's Under-20's. He is a product of Norwich's youth academy, and previously scored in the FA Youth Cup final against Chelsea back in 2013.
The move will see Murphy reunited in the Premier League with twin brother Jacob, who currently plies his trade in the north east with Newcastle.
Murphy may not be the only high profile departure from Carrow Road this summer, with playmaker James Maddison understood to be a target for a number of Premier League clubs.
Liverpool and Leicester are among those to be linked with a move for Maddison, with the Reds now looking for alternative attacking midfield options following the collapse of Nabil Fekir's proposed move to Anfield.