Mr Bercow, who has been in the role since 2009, will take the chair for the last time on 31 October.
He will formally resign as an MP on 4 November, in keeping with his two immediate predecessors.
Mr Bercow announced on Monday that he would stand down after 10 years in the role, which involves presiding over proceedings in the Commons.
He has been seen as a champion of backbench MPs and their efforts to hold the government to account, particularly on Brexit.
But critics accused Mr Bercow of straying out of the bounds of his authority and raised questions about his impartiality following a number of rulings which were considered to favour Remain supporters.
He survived numerous attempts to remove him from the chair, as well as revelations about his expenses and allegations of bullying, which he denied.
On Wednesday he warned Boris Johnson against complying with legislation passed by MPs to try to avoid a no-deal Brexit at the end of next month.
Mr Bercow said the prime minister would be acting like a “bank robber” – and pledged to allow “additional procedural creativity” to stop it from happening.
The election of his replacement will be overseen by Conservative MP Ken Clarke, the Father of House (longest-serving male MP).
Nominations have to be submitted between 9.30am and 10.30am on the day of the election, with the election the first order of business when proceedings begin at 2.30pm.
Mr Clarke will be in the chair.
Any MP can stand in the election, although if a minister or opposition frontbencher opted to do so, they would be expected to resign from their role.
Each candidate will make their pitch to MPs, with the order being selected by ballot.
MPs will then vote in secret.
Any candidate who wins 50% of the vote will emerge victorious, or successive ballots will be held to whittle down the candidates one by one.
The winner, who will then become the Speaker-elect, will attend the Lords Commissioners in the Lords to receive Royal Approbation.
Several candidates have put themselves forward for the job.
Deputy speaker Lindsay Hoyle, Labour MP Chris Bryant and Conservative MP Sir Edward Leigh have all said they will stand to succeed Mr Bercow.
Harriet Harman has also confirmed she will be standing.
The former deputy Labour leader told Sky News it is “time for another woman” in the speaker’s chair.