The 25-year-old's current deal was up at the end of the current season but Leeds have now tied down the defender until the end of 2020-2021.
Cooper follows Gaetano Berardi, Ronaldo Vieira, Kalvin Phillips, Lewie Coyle, Bailey Peacock-Farrell and Tyler Denton in securing new deals at Elland Road since the end of last term.
A number of other Whites players are out of contract next summer – including Eunan O’Kane, Rob Green, Stuart Dallas, Liam Bridcutt and Souleymane Doukara.
Leeds are also in talks with O'Kane about extending his present deal.
Cooper joined Leeds from Chesterfield for £600,000 in August 2014. The defender has since made 91 appearances for the Whites, scoring twice.
Cooper - who has previously been called up to the Scotland national side through his grandparents - captained United in last Sunday's season opener at Championship hosts Bolton.
The 25-year-old also wore the skipper's armband on a regular basis last year as vice captain to last season's club captain Liam Bridcutt.
The defender was rested for Wednesday night's first round Carabao Cup clash against Port Vale but is set to partner the back-from-suspension Pontus Jansson in Saturday's Championship clash with Preston North End at Elland Road.