The Lib Dems say more than 10,000 people have applied to join the party since the UK voted to leave the EU.
The party launched a campaign after the Brexit vote, using the hashtag #Wearethe48 - a reference to the 48% of people who voted to remain in the EU.
Leader Tim Farron says the result is "reversible" and said he would campaign to keep the UK in the EU at the next election, whenever it takes place.
Senior Tory and Labour figures insist the result must be respected.
Mr Farron, whose party has traditionally been the most pro-EU and backed a Remain vote, said the Lib Dems had seen an "enormous uplift" in support in the aftermath of the UK's decision to leave the EU.
The party says new members have been joining at nearly one a minute since the Brexit vote - swelling the party's membership ranks to more than 70,000.
The party, which served in coalition government between 2010 and 2015 but was reduced to eight MPs at the last election, has made a "clear and unequivocal" promise to campaign for the UK to remain in the EU at the next election.
The poll is not scheduled to take place until 2020 but some commentators believe the Brexit vote and the election of a new prime minister to succeed David Cameron may bring this forward.
Mr Farron has said a snap election later this year could be "a golden ticket to undoing the chaos" seen in recent days.
He has appealed to like-minded individuals in other parties to join forces to make the case for remaining in the EU - or at the very least retaining key elements of the UK's current arrangements in Brexit talks over the next few years.
Speaking in the House of Commons on Wednesday, Mr Farron said whatever deal the UK agreed with the EU on the terms of its exit, young people who voted overwhelmingly to remain in Europe must be protected.
"Given three-quarters of the young people of Britain voted to remain in Europe, they should be permitted, as far as possible, to remain in Europe," he said. "What can be done to make sure young people are allowed access even over and above those of the rest of us?"
In response, David Cameron said it was important that young people should have the opportunity to travel, work and study in the EU and the government would be considering the impact of Brexit on educational programmes like the Erasmus scheme.
The Lib Dems' membership fell sharply after the party went into coalition with the Conservatives, dropping from about 65,000 in 2010 to about 42,000 in 2014.
But it recovered after its 2015 election setback. At the time of last year's conference, the party had about 61,000 members.