The Prime Minister needs a majority of two thirds for it to go ahead, almost three years earlier than planned.
Parliament will dissolve on May 2 and formal campaigning will begin.
"It's about providing the strong and stable leadership this country needs to take Britain through Brexit and beyond, it's about strengthening our hand in the negotiations that lie ahead, and it's about sticking to our plan for a stronger Britain that will enable us to secure that more stable and secure future for this country and take the right long-term decisions for the future".
May is hoping to gain a bigger majority in Parliament for her Conservatives.
"If we're negotiating at a point that is quite close to a general election, I think the Europeans might have seen that as a time of weakness when they could push us", she explained.
May surprised allies and opponents on Tuesday when she announced her plan to bring forward an election that was not due until 2020, saying she needed to avoid a clash of priorities in the sensitive final stages of the two-year Brexit talks. Leaders of European Union states are due to adopt negotiating guidelines at an April 29 summit, and the bloc will prepare detailed plans for the talks with Britain by late May.
Currently, the Conservative Party has a narrow majority of 330 of the 650 seats in the House of Commons.
Speaking earlier, the premier suggested she won't use the election to give voters more detail about the kind of Brexit she wants, instead asking them to trust her to deliver.
The lawmakers approved the proposal, 522-13, after 90 minutes of debate to move the election up three years in a bid by the Conservative Party to expand its role in government and give better clout in negotiating Brexit.
The chief of the EU executive Jean-Claude Juncker and British Prime Minister Theresa May had a phone call on Tuesday evening, following May's call for early elections in June, a European Commission spokesman told a news conference.
Scottish First Minister Nicola Sturgeon described the election call as "a huge political miscalculation by the Prime Minister" which would allow the SNP to reinforce its democratic mandate to stage a second referendum on independence.
May wasted no time, going from the vote in Parliament to kick off her campaign with a speech in to supporters northwestern England.
The prime minister formally ruled out taking part in televised head to head debates before the June 8 election in a BBC interview yesterday.
Lib Dem leader Tim Farron says only his party can stop Theresa May winning the election.
"Can the PM tell the people why she is running scared of a televised debate with Nicola Sturgeon?" he added, to which May replied: "I can assure the right honourable gentleman that I will be out there campaigning in every part of the United Kingdom, taking out there our proud record of a Conservative government that has delivered for every part of the United Kingdom".
But if May can withstand the public scorn, she doesn't have much incentive to show up for a debate - her party's already the heavy favorite to carry the election.