Lord Rothermere, chairman of Daily Mail and General Trust (DMGT), said on Wednesday that Verity will take over as editor of Mail Newspapers, which includes overall responsibility of the Daily Mail and The Mail On Sunday.
Mr Verity has been editor of the Mail on Sunday for the past three years while Mr Greig was editor of The Mail On Sunday for the previous seven years and has spent the past three as editor of the Mail.
Mr Greig, 60, was editor of the Evening Standard from 2009, director of the Standard and The Independent from 2010, and editor of the Mail on Sunday from 2012 before he took over from Paul Dacre as editor of the Daily Mail in 2018.
Lord Rothermere said: “Under Geordie’s leadership, the Daily Mail has continued to inform and entertain millions of readers with the very best journalism, becoming the biggest-selling newspaper in the UK and winning multiple prizes for Daily Newspaper of the Year.
“Geordie has been an outstanding editor of the Daily Mail and, before that The Mail on Sunday, and I thank him for his contribution over the last decade.”
Mr Greig, who joined the Daily Mail in 1983 as a junior reporter, will become a consultant editor, Lord Rothermere said.
Mr Greig said: “I am grateful to Lord Rothermere for 10 extraordinary years as editor of his newspapers.
“I thank everyone who has worked with me; my colleagues have been heroic and inspiring.
“I wish my successor Ted Verity good luck and also continued good fortune to The Mail.
“I look forward to new opportunities ahead and will bring the best of what I learnt from my years at The Mail on which I first joined in 1983 as its most junior reporter on the graveyard shift.”