The player, who is entering the final year of his contract, expressed a strong desire to take the step up to the Premier League and test himself at the highest level.
The fee is to remain undisclosed and the player has been given permission to discuss personal terms and undergo a medical.
It is expected Brayford will complete the formalities of the transfer on Friday.
The 25-year-old, who can play right-back or fill in at centre-half, will leave Pride Park after four seasons since joining from Crewe Alexandra in 2008.
He made 117 appearances for the Rams scoring all three goals last season.