Reps. Kevin McCarthy, R-California, Jason Chaffetz, R-Utah, and Daniel Webster, R-Florida, are the three candidates vying for the post, and the winner becomes the favorite to become second in line to succeed the President of the United States.
But Thursday's vote inside the House GOP conference is just the first step. The candidate who gets the Republican party's internal nod still has to be approved by the full House of Representatives on October 29. And that's where things can get tricky.
If the Republican nominee can't garner 218 votes on the House floor, then Boehner will remain the speaker. And the potential for multiple rounds of votes on the House floor could open up the election to other candidates beyond the three that are in the race now. It would also prolong the deeply divisive and public process for House Republicans, who are hoping to chart a new path forward and prove they can make the dysfunctional Capitol work.
Here are the steps:
The three candidates will make their pitch to GOP colleagues at a "candidate forum" on Thursday morning in a conference room in the basement of the Capitol. Each gets three minutes to make a speech before answering questions from members.
House GOP Conference Secret Ballot
At noon, the 247 members of the House Republican conference gather in the ornate Ways and Means Committee room to vote.
Under the House GOP conference rules, the three candidates are not allowed to make their own speeches. Instead each can designate one supporter to make a three-minute address nominating them for the post. Then up to two additional supporters can speak for another minute each on the candidate's behalf.
To win the GOP nomination, a candidate needs a simple majority of all House Republicans -- or 125 votes. (That number could change if any House Republicans are absent or opts not to vote in the election.)
Boehner plans to vote for McCarthy before heading to New York to tape an appearance on "The Tonight Show," according to a spokesman.
The delegate from American Samoa, Amata Radewagen, who doesn't get a vote on the House floor, does get to cast a vote for speaker inside the conference meeting.
Three members serve as "tally clerks" and collect the ballots and count how many votes each candidate receives.
Once all the ballots are counted, a representative of the conference will announce the results, along with the vote totals.
If no candidate gets a majority of the conference on the first vote, a second ballot circulates with the names of the top two vote-getters, and a winner is announced after those ballots are counted.
Election on the House Floor -- October 29
The new speaker can't take the gavel from Boehner until the full House of Representatives votes.
Unlike the private contest on Thursday, the floor vote is covered live by C-SPAN's television cameras inside the House chamber.
Each member of Congress is called on in alphabetical order to stand and announce their choice for speaker. The winner must win the votes of a majority -- 218, if everyone in the House is present -- in order to win.
The vast majority of House Democrats are expected for to vote for former Speaker and current Minority Leader Nancy Pelosi.
House Republican conference rules require that GOP members support their party's nominee on the floor, but many conservatives have ignored that rule in recent elections. That's where any drama will occur.
If the GOP nominee fails to get a majority, the contest on the House floor could go to multiple ballots. Boehner will remain the speaker until a majority of the House votes to elect a new candidate.
The last time it took more than one ballot to elect a speaker was in 1923 when it took nine ballots over the course of three days.
And you don't need to be in the House to get the job. The Constitution does not require that the speaker be someone currently serving in Congress, but all who have been elected to the post have been House members. Former Secretary of State Colin Powell, Sen. Rand Paul and Sen. Jeff Sessions received votes in the January 2015 election
. And two years earlier, David Walker, the former head of the General Accounting Office, received one vote