Sir Ivan, who was appointed to the role of permanent representative by David Cameron in 2013, had been expected to play a key role in Brexit talks expected to start within months.
The Foreign Office said it would not give reasons for his departure at the moment.
Last month the BBC revealed he had privately told ministers a UK-EU trade deal might take 10 years to finalise.
He told them this was also the view of the other 27 member states.
BBC Brussels correspondent Kevin Connolly said it appeared there had been “some failure of synchronisation” between Sir Ivan and the UK government.
‘Difficult time’
Sir Ivan had been due to leave his post in November, the Financial Times reported.
Labour MP Hilary Benn, who chairs the Brexit select committee, said his resignation had come at a “crucial” point and urged the government to “get its skates on” in finding a replacement.
“It couldn’t be a more difficult time to organise a handover,” he added.
Mr Benn told BBC Radio 4’s The World at One the permanent representative’s job was to convey the view of the UK to the 27 member states, as well as “honestly and fearlessly reporting back” what those countries in turn said about the negotiations.
Prime Minister Theresa May says she will trigger formal talks between the UK and the EU by the end of March, setting in place a two-year negotiation process.
Sir Ivan is a veteran civil servant whose previous roles include private secretary to ex-chancellor Ken Clarke, principle private secretary to ex-PM Tony Blair and Mr Cameron’s Europe adviser.
He was criticised in some quarters for “pessimism” over Brexit after his advice to ministers on the negotiating timescale was reported.
UKIP donor and Leave. EU chairman Arron Banks said Sir Ivan was “yet another of the establishment’s pro-EU old guard” and welcomed his resignation.
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