Coutts, 23, joins on a three-year deal and becomes boss Nigel Clough's second signing of the summer following the arrival of winger Michael Jacobs.
The Rams claim to have beaten off competition from several Championship clubs to secure the signature of a player who can operate on the wing as well as in the middle.
"We are delighted to secure the services of Paul as he is someone who has been on our radar for some time," Clough told the club's official website.
"He is still young but he knows the division well from his time at Peterborough and Preston and we're all really looking forward to working with him."
Coutts made 86 appearances for the Lilywhites after arriving in January 2010 and scored five goals.