Mrs May, addressing voters as she stood surrounded by party activists and supporters, said: "Only you can give us the mandate, so vote for a strong and stable leadership in this country".
The House of Commons backed the prime minister by a margin of 522 votes to 13, above the two-thirds majority needed, as Labour and the Lib Dems supported the move.
Parliament will still sit for another fortnight, but party leaders wasted no time in hitting the campaign trail on Wednesday evening.
The UK prime minister, who until very recently opposed holding a referendum, said that the vote is necessary to strengthen her position at the Brexit negotiating table.
Elections are now set for 2020, just a year after the scheduled completion of Brexit talks.
"That would be in nobody's interest", May said.
Now that lawmakers have approved the election, Parliament will be dissolved at midnight on May 2, 25 working days before election day.
The opposition Labour Party and the Liberal Democrats welcomed May's surprise call on April 18 for the early poll, while the Scottish National Party (SNP) signaled that its deputies would abstain in the vote.
Facing criticism from within his own party over his leadership style, Mr Corbyn will on Thursday seek to make a virtue out of his refusal to conform to political norms.
Though May has been cautious in detailing her Brexit aspirations, traders think a big victory for her in the election could give her ammunition in dealing with those within her own Conservative Party who are urging a complete, "hard" divorce from the European Union - even if that means new tariffs and an exclusion from the bloc's huge single market.
The paper cited polling data from YouGov that suggested the Conservatives were on course to win a majority of 114 House of Commons seats on June 8.
Liberal Democrat leader Tim Farron said that, for May, calling the election is "the political equivalent of taking candy from a baby".
May, Britain's second female prime minister, also has strong popular support for her handling of the political quake unleashed by Brexit.
The Liberal Democrats won a ninth seat in parliament in a by-election in Richmond in December.
The June election would be the third time in two years voters are sent to polling booths, after a May 2015 national election and a June 2016 referendum on European Union membership.
"Brexit isn't just about the letter that says we want to leave".
In short, May is trying to make sure she gets a hard Brexit passed since the people voted to leave the EU.
Initially, EU officials had said that the talks could start in late May once a detailed negotiating mandate had been agreed among the EU's 27 other members.
However, it is likely to take a few days, assuming victory on June 8, for May to confirm her negotiating team; it is now led by Brexit Secretary David Davis, who unlike May is a long-time opponent of Britain's membership of the Union.
Mrs May added: "I believe in campaigns where politicians actually get out and about and meet with voters".
Alex Massie in The Spectator believes the general election will first and foremost be a vote on Scottish independence, saying "May can not win a mandate for herself while then denying a mandate to the party that wins the Scottish portion of this election".
SNP leader and Scottish First Minister Nicola Sturgeon also argued that "broadcasters should empty chair her and go ahead anyway".
He said Mrs May's U-turn on her previous insistence that she would not call a snap election showed she could not be trusted.