The news was posted on twitter by current President Felipe Calderon and confirmed by a spokeswoman in Calderon's office.
De la Madrid was president from 1982 to 1988, a period that included severe economic crises and an earthquake that devastated Mexico City.
The cause of his death has not been announced, but the former president had been hospitalized for respiratory problems since last year.
Several false rumors about De la Madrid's death surfaced in December, and Calderon even sent an incorrect tweet on his official Twitter account at that time offering condolences to the former president's family. He corrected that earlier false report minutes later.
The Associated Press contributed to this report.