The ex-cabinet minister called for either Parliament or the public to be given the chance to have a straight vote between EU membership and a negotiated alternative.
Mr Miliband also issued a call for politicians from all parties to fight back against the “worst consequences” of last year’s vote to leave the EU.
He warned that Brexit is an “unparalleled act of economic self-harm” and that “politics and government are setting new standards for dysfunction” in his article for the Observer.
He said: “People say we must respect the referendum. We should. But democracy did not end on June 23 2016. The referendum will be no excuse if the country is driven off a cliff.
“MPs are there to exercise judgment. Delegating to Theresa May and David Davis, never mind Boris Johnson and Liam Fox, the settlement of a workable alternative to EU membership is a delusion, not just an abdication.”
He also praised Chancellor Philip Hammond for pushing for a post-Brexit transition deal with the EU.
Mr Miliband said: “I never thought I would say this, but Philip Hammond is also playing an important, even valiant, role.
“A transition of the kind he has advocated is vital.”
However, the former Labour politician’s intervention comes as Philip Hammond and International Trade Secretary Liam Fox today came together to declare that a post-Brexit transition would not be a “back door” to Britain remaining in the EU.
Mr Hammond and Dr Fox have claimed that the UK will leave the single market and customs union in 2019.
Papers published by the Government from next week, which lay the ground for the next round of talks, will cover Northern Ireland, availability of goods for the EU and UK and access to official documents post Brexit.
A second batch, to be released before the October meeting of the European Council in Brussels, will look at future partnership arrangements, such as UK proposals for a customs arrangement with the EU.