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 Brayford has been given permission to discuss personal terms and undergo a medical.
It is expected the 25-year-old will complete the formalities of the transfer on Friday.
Brayford, who can play left-back or fill in at centre-half, will leave Pride Park after four seasons since joining from Crewe Alexandra in 2010.
He has made 117 appearances for the Rams, scoring all three goals last season.
The Rams last month turned down a bid in the region of £1m from Wigan for the right-back.
The 25-year-old is entering the final year of his current contract at Pride Park and manager Nigel Clough had planned to discuss a new deal with the player next week.
A statement issued by Derby said: "After holding discussions with the player, who is entering the final year of his contract, the offer has been accepted after he expressed a strong desire to make the move and test himself at the highest level of English football.
"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.
"Derby are committed to continuing to strengthen the squad in advance of the
2013/14 season and expect additions to be made in due course."
Brayford joined Derby from Crewe in the summer of 2010 and was player of the year in his first season with the Rams.
The former Burton Albion man has made 118 appearances, all but one of them starts, and scored four goals during his time at County.