Jeremy Greenstock was born on 27 July 1943, son of John Wilfrid Greenstock and Ruth Margaret Logan. He was educated at Harrow School and Worcester College, University of Oxford, and in 1969 married Anne Derryn Ashford Hodges; they had one son and two daughters.

After a spell as an Assistant Master at Eton College (1966-69), Greenstock entered the Diplomatic Service (Nigeria desk) in 1969 and his career included the following posts; Middle East Centre for Arab Studies, (1970); Dubai, (1972); Private Secretary to the Ambassador, Washington [Sir Peter Ramsbotham and Peter Jay], (1974-78); Foreign and Commonwealth Office, Planning Staff, (1978); Personnel Operations Department, (1979); North East and North African Department, (1981); Counsellor (Commercial), Jiddah, then Riyadh [Saudi Arabia], (1983); Head of Chancery, Paris [France], (1987); FCO, Assistant Under-Secretary of State (Western and Southern Europe, including Bosnia [Bosnia and Herzegovina]), (1990); Minister, Washington [United States], (1994); FCO, Deputy Under Secretary of State, (1995); Political Director, (1996); British Permanent Representative to the UN, (1998); Special Representative, Baghdad [Iraq] (retirement postponed, 2003-4).