Brayford is now free to talk to the Welsh club after their offer, believed to be around B£2million, was successful.
The Rams last month turned down a bid in the region of B£1million from Wigan for the right-back.
The 25-year-old is 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 Pride Park.