The 27-year-old left-back joins on a three-year deal, becoming Frank Lampard's eighth summer signing at Pride Park.
Malone, who began his career at Wolverhampton Wanderers, has played for Bournemouth, Millwall, Cardiff City and Fulham.
In addition, the Englishman has also had loan spells with Southend United and Burton Albion.
"Scott Malone is a player that I have liked for a long time and we're really pleased to bring him to Derby County," Lampard told the official Rams website.
"He's an attacking left-back with lots of speed and with the way we want to play, the full-backs are very important for us.
"I have spoken before about it being important to have options across all areas and Scott provides another one for us, but I think it's also important to mention that Max Lowe has been fantastic in the games so far."
Derby kicked off their season with a 2-1 win at Reading on Friday night.