His departure follows recent problems with the Payments by Results tariff, which had to be withdrawn due to errors, and revelations over increasing levels of NHS overspends.
Sir Nigel said: 'I wish to acknowledge my accountability for problems just as I may take some credit for achievements.'
King's Fund chief executive Niall Dickson said that Sir Nigel was leaving the NHS in a much better state than when he took over and that responsibility for financial problems was shared with politicians.
'The manner and timing of his departure is not helpful,' said Mr Dickson.
'The last thing the NHS needs now is more instability.'
BMA chairman James Johnson said: 'There are clearly problems in the NHS and we look forward to working with his successors to help tackle these.'
Mike Farrar, chief executive of South Yorkshire SHA, said: 'Sir Nigel established a good platform for reform.'
Sir Nigel will be replaced in the interim by Sir Ian Carruthers, who is currently acting director of commissioning and joint chief executive of Dorset and Somerset SHA and Hampshire and Isle of Wight SHA. He has served in a number of modernising roles at the DoH.