The journalist and peer died following a short illness, according to his son, MP Jacob Rees-Mogg.
Jacob told the newspaper: "It has been a mercifully short illness. He died very peacefully and a member of his family was with him. He was very prepared for it."
Lord Rees-Mogg joined the Financial Times after leaving Oxford University and later moved to a three-year deputy editorship at the Sunday Times.
He became editor of The Times in 1967, replacing Sir William Haley, and headed the daily broadsheet through a difficult 14 years in its history.
The newspaper was not produced for 11 months in 1978 to 1979 following a dispute over new technology. He was replaced as editor by Harold Evans in 1981, after Rupert Murdoch bought the Times titles from Lord Thomson.
During his time as editor, he criticised Rolling Stones frontman Mick Jagger's 1967 drug-related jail sentence.
The publication noted that his opinion would often change on major issues. Lord Rees-Mogg defended himself over the claim, saying: "It's not my job to be right. It's my job to be interesting."
Lord Rees-Mogg continued as a journalist until his death and wrote his last column for The Times two weeks ago, Jacob said.
He added: "I had the greatest father anyone could ever want, who always encouraged his children in the different things that they did.
"He had the most extraordinary knowledge of almost every subject you could ever ask him about, and had this fascinating position in British public life for the last 60 years.
"We are all enormously proud of him and all that he did; and that he found time to be the most active and loving father."
Lord Rees-Mogg was also a former chairman of the Arts Council and vice-chairman of the BBC.