Officials say Evert had been treated for weeks in intensive care for breathing problems. His death was announced in Parliament by Health Minister Andreas Loverdos.
Evert was chairman of Greece's New Democracy party from 1993 until its fall from power in 1997. He held a number of Cabinet positions - including the finance portfolio.
An economist and animal lover who kept several dogs and a pet monkey, Evert was first elected to Parliament in 1974, after the collapse of the 1967-74 military dictatorship. He served as mayor of Athens from 1987-1989, founding Greece's first municipal radio station.
Evert is survived by his widow, photographer Liza Evert, and their two daughters. Funeral arrangements have not been announced.