May said on Tuesday that she had been reluctant about asking parliament to back her move to bring forward the election from 2020, but decided it was necessary to win support for her ruling Conservative Party's efforts to press ahead with Britain's departure from the EU.
The motion passed with 522 members of parliament in favour and 13 against - well above the required two-thirds majority.
Opening the debate on a snap poll, Mrs May said it was time "put our fate in the hands of the people and let the people decide".
According to those predictions, the Conservatives are on course to gain the strong mandate that May seeks in order to push her Brexit agenda through parliament.
An early ballot, which May wants to hold June 8, will give the prime minister - or her replacement - more time to implement Brexit before another election.
May said the early vote is necessary to ensure that her government can "strengthen our position in these negotiations".
"That would be in nobody's interest", May said.
If the election is approved Wednesday, Parliament will be dissolved on May 2, sparking nearly six weeks of campaigning.
Despite Corbyn's bravado, his party is demoralized and divided under his left-wing leadership and is expected to fare badly.
"We welcome the general election", said the Labour Party's Jermey Corbyn, triggering guffaws and laughter.
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Liberal Democrat leader Tim Farron accused May of putting her party above the country and said she was running scared by not accepting the challenge of TV debates.
Scoring points off May's government is both too easy - they are barely holding it together by any normal governmental standards - and too hard; the levers by which they are held to account aren't working, and attacks do nothing to douse their impunity.
But as she spoke Mr Corbyn explicitly ruled out any post-election coalition with the SNP, insisting that he would not do a deal with Nicola Sturgeon's party to forge a so-called "progressive alliance", as hers was not a progressive party.
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.
It's likely in the 20 bills coming up that about three quarters will be Brexit-related, so you can understand she wants to have a mandate and a larger majority. "It's about ... getting the right deal from Europe".
The two-year exit negotiation process began last month when May triggered Article 50 of the Lisbon EU treaty.
Schinas and other European Union officials have said they expect draft Brexit guidelines to be adopted by the leaders of the other 27 European Union countries at an April 29 summit. The premier has already backed out from televised debates.
"The UK elections do not change our EU27 plans", Preben Aamann, a spokesperson for European Council President Donald Tusk, said in a statement on Tuesday.
May, who has described herself as "not a showy politician", also said she would not take part in television debates before the election, preferring to talk directly to voters.