He said in a statement: "I accept responsibility and have decided to resign in the best interests of English Heritage."
The move followed a report which English Heritage said "concerned alleged administrative irregularities by Mr Green in charge of his duties".
Sir Jocelyn Stevens, chairman of English Heritage, accepted the resignation of Mr Green, 52, who joined the organisationfrom ScotRail, where he was director, on 1 March 1995.
The appointment was a surprise. Mr Green' s acceptance of the job was seen at the time as a vote of no-confidence in the Government's rail privatisation plans, about which he had become highly critical. Ministers had hoped that Mr Green would launch a management buy-out of ScotRail and lead it into a successful new existence in the private sector
He was one of British Rail's most experienced and highly regarded managers, having set up Network SouthEast and raised the profile of InterCity and then ScotRail. He was regarded by many as a miracle worker on the railways who actually improved punctuality and cleanliness.
As chief executive of English Heritage, Mr Green has been less prominent, however.
Jane Sharman, the organisation's director of conservation, has been appointed acting chief executive and acting accounting officer. A spokeswoman for English Heritage said at its offices in Savile Row, London: "We cannot make any more comment on the resignation."
The organisation is the Government's official adviser on historic buildings and sites, and manages more than 400 properties.
Mr Green, who graduated in history at Oriel College, Oxford,was head- hunted by English Heritage after a brilliant 30-year career on the railways. He spoke of his love of history and historic places when he took over and launched several high-profile initiatives, such as a plan to preserve more of the country's battle sites.
Mr Green was brought up in Richmond, Surrey, where his parents were teachers. His love of trains began when he commuted to St Paul's School in the centre of London.
When he graduated in 1965 he briefly considered a career in the Ministry of Transport. Instead, he opted for management training at British Rail. There, he rose through theranks rapidly, showing a flair for organisation.Reuse content