Grant, whose contract at Turf Moor expired this summer, was offered new terms by the Clarets.
However, for personal reasons the 30-year-old has elected to re-join his first club on a three-year deal.
Burnley manager Sean Dyche said: “Lee was signed at a significant cost to the club and was one of our biggest earners.
“We were keen to retain his services and made an offer to do so, but the lure of moving back to Derby, where his family are based, ultimately proved too good to turn down and we are sorry to lose him.
“However, we wish him well and thank him for his contribution to the club.”
Grant, who was last week voted as the fans’ player of the year, made 130 appearances in his second spell with Burnley, having previously joined on loan in the 2005/06 campaign,