The UK's Petitions Committee said the debate would be held on September 5 as a "huge number" had signed it but it would not influence any change in the rules of the referendum already held on June 23, when Britain voted to leave the European Union by 52 to 48 per cent.
In a statement, the House of Commons Petitions Committee said a debate on the petition would allow MPs to "put forward a range of views on behalf of their constituents" and a government minister would respond to the points raised.
"It will be up to the government to decide whether it wants to start the process of agreeing a new law for a second referendum."
The online petition, set up by William Oliver Healey, gained more signatures than any other on the parliamentary website in the wake of Brexit.
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Before the result was declared on June 24, just 22 people had signed it.
The petition, set up on 25 May before the referendum, states: "We the undersigned call upon HM Government to implement a rule that if the Remain or Leave vote is less than 60 per cent, based on a turnout of less than 75 per cent, there should be another referendum."
The referendum saw 17.4 million (51.9 per cent) votes cast to leave the EU, compared with 16.1 million (48.1 per cent) for Remain, with a turnout of 72.2 per cent, according to the UK's Electoral Commission.