The online campaign, set up by French translator and hardcore Remainer Anne Greaves, has amassed huge support since it was set up just before Christmas.
It demands MPs be given the option of overturning the referendum result and axing Brexit if they do not like the final deal.
After a Commons defeat for Theresa May by rebel Tories last month, MPs will get a “meaningful vote” on the final deal with the EU.
But they have been warned even if they vote down the agreement, it simply means the UK will crash out of the bloc without a deal.
The petition calls the meaningful vote a “Hobson’s Choice” – the option of accepting what is available or nothing at all.
Ms Greaves wrote: “Parliament’s vote on the Brexit deal must include an option to remain in the EU.
“A lesser of two evils choice between a bad deal and no deal is not acceptable.
“Our country deserves better than Hobson’s choice, and our MPs should be allowed to vote with their conscience to deliver what they believe is best for the country.”
More than 47,000 people have signed the petition in just a few days, but online data shows thousands of those supporting it do not even live in the UK.
Those hijacking the vote include nearly 900 people in France, over 450 in Spain, 170 in Germany and 77 Belgians.
People living in far-flung Nicaragua, Guinea, Kenya and the tiny island of Tuvalu have signed up.
Of those who do live in the UK, the vast majority live in the south, with a high proportion in Remain-voting London.
Parts of Oxfordshire and Cambridgeshire – including Brexit Tory rebel Heidi Allen’s constituency – also have a high build-up alongside hipster coastal town Brighton.
But there is very little support in the Midlands and further north, with Scotland also snubbing the campaign, aside from in Edinburgh.
If there are enough signatures to hit 100,000, the petition will be considered for debate in Parliament.
In its response to the petition, the Department for Exiting the European Union dismissed the Remainers’ latest wheeze.
They wrote: “The British people voted to leave and the Government will implement their decision.
“The vote on the final deal will give Parliament the choice to accept the agreement or leave the EU with no agreement.
“The result of the referendum held on 23 June 2016 saw a clear majority of people vote to leave the European Union.
“Parliament overwhelmingly confirmed the result of the referendum, on 8 February, by voting with clear and convincing majorities in both of its Houses for the European Union (Notification of Withdrawal) Bill.
“The Government is clear that it is its duty to deliver on the instruction of the British people and implement the result of the referendum.
“The Government has committed to hold a vote on the final deal in Parliament as soon as possible after the negotiations have concluded.
“The terms of this vote are clear; Parliament will have the choice to accept that deal or to move ahead without a deal.
“We are confident that we will get the best possible agreement and one which Parliament will want to support.”