Video report by ITV News Political Correspondent Daniel Hewitt
Ms Swinson will be the first female head of the Liberal Democrats, after holding the position of deputy leader for two years.
In her victory speech, Ms Swinson said she was "delighted, honoured and absolutely over the moon" to be elected, and has vowed to stop Brexit.
"You have put your trust in me not only to lead the party, but also to lead the grow the bigger open liberal movement our country so desperately needs," she said.
"Liberalism is alive and thriving."
She added: "In the face of nationalism, populism, the catastrophe of Brexit, the two old parties have failed.
"We believe the UK’s best future is as members of the EU, and that’s why as your leader, I will do whatever it takes to stop Brexit."
Jo Swinson says: "I will do whatever it takes to stop Brexit"
Ms Swinson will be replacing Sir Vince Cable - leader of the party since 2017 - and will be taking over a party different to the one her predecessor had inherited.
When Sir Vince stepped up as leader, the Liberal Democrats were recovering from their poor performance in both the 2015 and 2017 elections.
Fast-forward to 2019, and the party has been re-energised by their boost in popularity due to their strong anti-Brexit stance.
The party made huge strides in the European elections, which saw them win over 20 per cent of the vote share and 16 MEPs enter European parliament.
The Liberal Democrats' clear Brexit messaging also helped them win votes in the local elections.