The former prime minister said an extension to Article 50 was “inescapable” to avoid chaos on the scheduled March 29 departure date from the European Union.
He said that extending the period by 12 months would allow MPs to listen to the public through a “citizens’ consultation” on the detail of current Brexit proposals and the alternative options.
Delaying Brexit to find a proper resolution was the best way to restore national pride, he suggested.
Mr Brown’s call is part of a concerted effort involving business leaders, union chiefs, community representatives and senior politicians to call for a delay.
Prime Minister Theresa May has promised MPs a vote on calling for an extension to Article 50 if they reject her Withdrawal Agreement and a no-deal Brexit in crunch votes next week.
But she has suggested that any extension must be short, in part to avoid the UK taking part in European elections which will see newly-elected MEPs take their seats in July.
Mr Brown said a short extension would not allow enough time for a considered assessment of the options available to the UK.
He said: “The logic of extending Article 50 is now inescapable to avoid chaos on March 29 and prevent an impending national political disaster.”
Mr Brown said the “ill-thought-out” approach to Brexit had left the economy “drastically ill-prepared”.
He added: “Decades from now a new generation will look back with stunned disbelief at the way the Brexit debate has been conducted so far.”
It was “near impossible” to pass the necessary legislation required for Brexit by March 29 and Mr Brown said there was support in Europe for an extension.
“Leaders agree with their chief negotiator Michel Barnier that an extension has ‘become almost inevitable’ and that they have to try to overcome the technical difficulties of British participation in the European elections and ensure an extension substantially longer than three months,” he said.
“It is now clear that Article 50 should be extended, perhaps for a year, not as a delaying tactic or just for MPs to rerun the old arguments in the Westminster bubble, but for a positive purpose - to allow Parliament to reflect - and to begin to bring the country together again.”
Mr Brown said the citizens’ consultation should cover issues including immigration and sovereignty and the “options available across Europe and for us of addressing these”.
He added: “Brexit must be delayed long enough for us to reach proper decisions - and restore the nation’s hope and its pride.”
Business figures backing the call include former Sainsbury’s boss Justin King, Lastminute.com co-founder Baroness Lane-Fox, former BT chairman Sir Mike Rake and former City minister Lord Myners, Mr Brown’s office said.