The Speaker keeps order in Commons debates and calls MPs to speak. Eight candidates are in the running, including ex-deputy Labour leader Harriet Harman and current deputy Speaker Sir Lindsay Hoyle. At 14:30 GMT the candidates will make short speeches in the Commons after which MPs will cast their votes.
How will the vote unfold?
MPs have 20 minutes to vote in a secret ballot, and it will take about an hour to count them. If no candidate receives more half of the votes, the individual who receives the least votes will drop out, as will anyone who obtains less than 5% of the total cast. After each round, there will be a 10-minute period for candidates to withdraw. MPs will then continue to vote until one candidate obtains more than half of the votes. The process will be overseen by Ken Clarke, who as Father of the House is the long-serving MP in the Commons.
Who is in the running?
The eight candidates are:
Chris Bryant - former minister and shadow Commons leader; Labour MP for Rhondda since 2001
Harriet Harman - former minister and deputy Labour leader; Labour MP since 1982, for Peckham and its successor constituency Camberwell
Meg Hillier - chairwoman of the Public Accounts Committee and former minister; Labour MP for Hackney South and Shoreditch since 2005
Sir Lindsay Hoyle - elected Labour MP for Chorley in 1997; elected deputy Speaker in 2010
Dame Eleanor Laing - elected Conservative MP for Epping Forest in 1997; elected deputy Speaker in 2013
Sir Edward Leigh - Conservative MP for Gainsborough since 1983; former chairman of the Public Accounts Committee
Shailesh Vara - Conservative MP for North West Cambridgeshire since 2005; former Northern Ireland minister
Dame Rosie Winterton - elected Labour MP for Doncaster Central in 1997; former Labour chief whip; elected deputy Speaker in 2017
BBC parliamentary correspondent Mark D'Arcy said most observers believed Sir Lindsay was the frontrunner.
He has been Mr Bercow's senior deputy for years.
"As Chairman of Ways and Means, he chairs Budget debates and selects amendments for committee stage proceedings on bills, and has had plenty of opportunity to demonstrate his credentials," our correspondent says.
What is the Speaker's role?
The role of the Speaker has come under increasing scrutiny over the past few years - and Mr Bercow has been both praised for boosting the influence of backbench MPs and criticised for stretching parliamentary rules. Some have also accused him of not being impartial when it comes to Brexit.
The Speaker is responsible for choosing which amendments can be voted on - a power that has proved particularly significant in the Brexit process.
He is also in charge of upholding parliamentary rules, and Mr Bercow twice angered some MPs by refusing to allow the government to hold another vote on an already rejected Brexit deal.
The Speaker can also permit MPs to ask urgent questions whereby government ministers are summoned to the House of Commons over a time-sensitive or important matter.
During his years in the role, Mr Bercow dramatically increased the number of urgent questions asked.
Source: BBC NEWS