Moore stepped up to the editor's chair in 1995, following Max Hastings' move to edit the Evening Standard. He began his career at the paper as a reporter in 1979, leaving in 1984 to edit the Spectator for six years before arriving to edit sister paper the Sunday Telegraph in 1992 for three years.
Lord Black, chairman of Telegraph-owner Hollinger, said: "Charles Moore has been an outstanding and successful editor and we part with him with reluctance."
He is to be succeeded by Martin Newland, 41, previously deputy editor of the National Post in Canada and a former home editor of The Daily Telegraph.
"Martin Newland will, I am sure, uphold the high standard of Bill Deedes, Max Hastings and Charles Moore. He is a Telegraph veteran who was an important part of the great success of the National Post. Martin is an outstanding journalist," Lord Black said.
There was speculation that Moore had clashed with Lord Black over issues of strategy as the Daily Telegraph's circulation dropped below the 1m mark.
Elsewhere, it was being reported that Moore's departure was hastened over fears relating to the health of Lady Thatcher.
The elevation of Newland does not affect Sarah Sands, who continues in her role as deputy editor of The Daily Telegraph, although she is to take on editorship of the daily paper on Saturday.
Talk of Moore's departure is understood to have surfaced at the Labour Party Conference last night, forcing the Telegraph Group to issue a statement this morning.
In the statement, Lord Black paid tribute to Moore's achievements as editor, including the modernisation of the paper to make it more appealing to a wider audience and most recently by hiring columnists, including 'Trainspotting' author Irvine Welsh, without alienating its traditional readers.
"In his tenure, he led the newspaper to a successful outcome of the price and circulation war, and to a substantial modernisation, while being faithful to the newspaper's best traditions," Lord Black added.
Although standing down as editor, Moore will continue at the paper as group consulting editor and a columnist.
"It has been an honour to edit The Daily Telegraph for eight years. It is the greatest newspaper in this country. I am delighted to be able to continue in my new role and leave the paper in excellent condition and the editorship in very capable hands."
Moore's future at the paper has been under the spotlight for more than a year after he signed the deal to write Lady Thatcher's biography. He is understood to have secured a £750,000 advance for the book, which will not be published until after her death.
Boris Johnson, currently editor of The Spectator, had long been a favourite to succeed Moore, and Dominic Lawson, editor of the Sunday Telegraph was also thought to have had an outside chance.
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