Mr Hoyle has been a Labour MP for 22 years and was Mr Bercow's deputy from 2010, since when his distinctive Lancashire accent has rung out from the Speaker's chair. She entered the Commons in 1982 and served as Labour's deputy leader from 2007 to 2015.
The contest was between Lindsay Hoyle and Chris Bryant, both of the UK Labour party.
After three rounds of voting, seven candidates have been cut to two. "I will be transparent" said Hoyle speaking after the vote.
Sir Lindsay, who has held his Chorley constituency since 1997, commented on the Yorkshire roots of previous Speaker Betty Boothroyd, who was in the chair from 1992 until 2000 and witnessed the day's proceedings at Westminster.
Another woman in the running was Ms Eleanor Laing, Mr Bercow's No. 2 deputy since 2013.
Speaking to BBC Radio 4's Today programme, he said his priority would be to encourage tolerance and respect for all in the house.
MPs will vote for one candidate only and the ballot will remain open for around 20 minutes. Hoyle is the front-runner, winning 244 of the 575 votes cast in the second round.
Mr Bercow stepped down last Thursday after 10 years as Speaker.
But with a national election coming on December 12, the new Speaker's first job will depend on what government the public elect.
Two were eliminated in the first round but voting will continue until a victor secures more than half of votes, and can take their seat in the speaker's raised green chair.
The 62-year-old Lancastrian was chosen by MPs after he promised in a hustings speech to be "accountable" and ensure "fairness" in the Commons. Bercow, who was famous for his cries of "Order, order!" during chaotic parliamentary debates, broke with convention.
The centrist Liberal Democrats, who want to cancel Brexit, and the single-issue Brexit Party, which favors a no-deal exit from the bloc, are battling for British voters with strong views on whether the United Kingdom should quit the 28-nation EU.
Deputy Speaker Dame Rosie Winterton is the first of the seven candidates to make her case to become Speaker.
Mr Bryant asked for the "chance to serve" and pledged to "return to the rulebook, stitch it back together", acting as an "umpire not a player" in the role.
A British Conservative legislator has dropped out of the race to become the next House of Commons speaker. Like Bercow, he will run the daily business of the Commons.
Some politicians want to see a more cautious approach than that taken by Bercow, who prided himself on making the government answer to Parliament.
But critics accused him of subverting centuries of parliamentary tradition with the aim of frustrating Brexit.
Ballots will continue until either one MP wins more than 50% of the votes or only one remains.
He has presided over Prime Minister's Questions in the absence of the outgoing Speaker John Bercow and also controlled the Commons for every budget debate. She is the longest-serving female member of Parliament and is known as "Mother of the House".
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