Members voted for the new policy at their party conference in Bournemouth by an overwhelming majority.
Previously, the party has backed another referendum or “People’s Vote”, saying they would campaign to Remain.
She also confirmed that before an election is called, the Lib Dems would continue to work with other opposition parties to campaign for a further referendum, and to prevent a “dangerous” no-deal Brexit.
In his first speech at conference as a Lib Dem MP, Chuka Umunna – who left Labour over its Brexit stance – said it would give the party a “clear, unequivocal position”.
He said: “This [policy] will stop this national embarrassment and enable us to focus on the things that really matter.”
But former Lib Dem MP Simon Hughes had called on members to reject the policy, saying it would “take the focus away” from getting another referendum.
He said that as the first referendum was a decision made by the people, “it can only be the people who can reverse [it]”.
Home Secretary Priti Patel said the “entire machinery of government” was focused on securing that deal.
The PM is due to meet European Commission president Jean-Claude Juncker in Luxembourg this week, as negotiations aimed at securing a deal continue.
MPs passed a new law earlier this month that forces Boris Johnson to ask the EU for an extension to the deadline if a deal isn’t agreed by 19 October – two days after a key EU summit.
But the prime minister has said he would rather be “dead in a ditch” than ask for a delay, and the UK will leave the EU at the end of next month “whatever happens”.
The Lib Dems’ motion said that if the party became the government at the next general election, it would revoke Article 50 – the law that ensures the UK leaves the EU.
Earlier, Ms Swinson said: “If people put [the Lib Dems] into government… the stop Brexit party, then stopping Brexit is exactly what people will get.
Moving the motion in Bournemouth, Sir Vince said: “Brexit will make us poorer and risks breaking up our United Kingdom.
He added: “Jo [Swinson] is ready to steer us back into government as our new captain.
“And now, I am full of confidence and hope for our party and for our country.”