A spokesperson for the family says Bush died shortly after 10 p.m. Friday, about eight months after the death of his wife, Barbara Bush.
He was the 41st president and served from 1989 to 1993.
Eight years later his son George W. became the 43rd president.
The elder Bush saw his popularity swell with the U-S success in the Gulf War in 1991, but the Republican was defeated in his bid for a second term by Democrat Bill Clinton.
Bush had also been a World War II hero, Texas congressman, CIA director and Ronald Reagan's vice-president.
Only one other U.S. president, John Adams, had a son who also became president.