A majority of 509 with 522 MPs backing the move and just 13 opposing gave the Prime Minister the two-thirds majority needed to overturn the Fixed-Term Parliaments Act.
The Scottish National Party abstained from voting on the motion, but it was backed by most Labour politicians and the Liberal Democrats.
The Labour leader said it was a "chance to vote for a Labour government that will put the interest of the majority first".
Schinas said the negotiations had been due to begin in June even before his boss Jean-Claude Juncker had spoken Tuesday to British Prime Minister Theresa May in the wake of her shock call for an early election.
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.
She told BBC Radio 4's Today programme: "We won't be doing television debates".
"I believe that at this moment of enormous national significance there should be unity here in Westminster, not division", Ms May told Parliament.
"The public want us to actually deliver on leaving the European Union and they want us to build that stronger Britain for the future, beyond leaving the European Union".
The Prime Minister confirmed on Wednesday that she will not face Mr Corbyn and other party leaders in live TV debates in the run-up to the June 8 poll, insisting that campaigning should be about getting "out and about" meeting voters.
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.
Although the outcome of the vote was never in doubt, MPs used the debate to make party political points and to attack whichever party represents the greatest threat in their constituency.
Speaking on Facebook, Nick Coyne said: "Let's see how her Brexit negotiations go first, then have an election".
UPDATE 6.30pm: Theresa May asked voters for the mandate to lead post-Brexit Britain as she rallied Tory troops for the looming election campaign ahead.
Following considerable wrangling over formats, the 2015 election campaign saw one debate featuring Mr Cameron and Mr Clegg alongside Labour's Ed Miliband and leaders of Ukip, the Scottish National Party, Greens and Plaid Cymru, as well as a second debate with the five non-coalition parties and programmes in which Mr Cameron, Mr Clegg and Mr Miliband answered questions but did not debate face-to-face.
Now that lawmakers have approved the election, Parliament will be dissolved at midnight on May 2, 25 working days before election day.
"With a bigger majority she can afford more defections", Ford said, adding: "It would give May more freedom to compromise".
'It has been an honour and privilege to serve as MP for South Basildon and East Thurrock since 2010 and I will again put myself forward for election to represent our area, ensuring local people have a strong voice in Westminster.
Lib Dem leader Tim Farron says only his party can stop Theresa May winning the election.
MPs were also excited by the news that ITV will go ahead with a leaders' debate, despite May's confirmation on Wednesday that she will not take part in any.
May, previously the interior minister, took over as prime minister for David Cameron, who resigned past year after voters said Yes to Brexit.