Boris Johnson's top choice for the role cited "personal reasons", according to reports.
In a letter to the Financial Times, Dacre claimed the number of advertisers with the paper had fallen since Greig's appointment.
"Predictable DM turncoat codswallop."
Like him or loathe him, his exit marks the end of a remarkable era for the British media.
Georgie Greig takes over later this year.
Greig is currently editor of sister newspaper, The Mail on Sunday.
He actually likes Hugh Grant.
From Brexit and welfare to Stephen Lawrence and plastic.
One of Fleet Street’s most powerful figures to 'step back' from November.