He worked for the South East London and Deptford Mercury newspaper, the Daily Mail and Sunday Today, before joining the Sunday Times in 1987. He became the editor of Tatler magazine in 1999.

London Evening Standard

On 2 February 2009 it was announced by the Evening Standard that Greig had been appointed its editor, subject to ratification by the Editorial Committee. This announcement followed the announcement on 21 January 2009 by the Daily Mail group that its newspaper division, Associated Newspapers Ltd, had agreed the sale of a majority interest in the Evening Standard for a nominal sum to Evening Press Ltd, a company formed by Alexander Lebedev and his son Evgeny Lebedev and owned by Lebedev Holdings Ltd.

His first step as Evening Standard editor was to launch a series of "Sorry" advertisements across London, after market research showed the paper was deemed too negative and complacent about London under former editor Veronica Wadley's leadership, a move considered to be extremely daring.

In addition to his editorial duties, Greig has literary interests, for instance being an admirer of the work of Samuel Menashe and Anthony Trollope.

On 1 May 2005, The Observer newspaper termed Greig "Britain's most connected man".

Greig is also Vice-President of Kitab, the annual British-Indian Literary and Media Festival. He is also member of White's the London gentlemen's club.

He is married to Kathryn Terry, who is originally from Texas; the Greigs have three children, Jasper, and a pair of twins Octavia and Monica. They live in Notting Hill.

Greig's great-grandfather was Lord Mowbray, Segrave and Stourton, and members of his father's family have been royal courtiers for three generations.