The move was confirmed during a backbench debate on the row over Carol Mills' choice as preferred candidate.
Commons Speaker John Bercow decided recently to pause the process amid MPs' concerns about her suitability.
Mr Straw told MPs that it was "imperative" that the future status and remit of the job was agreed upon.
The clerk of the House is the principal constitutional adviser to the Commons, and adviser on all its procedure and business.
Paid Â£200,000 a year, he or she is also responsible for the overall administration of the House of Commons, including the signing of leases, contracts and public expenditure on Commons services.
MPs have questioned the selection of Carol Mills - who works in the Australian Parliament - to replace the former Clerk Sir Robert Rogers, who retired in July.
Speaking in a debate in the Commons, Jesse Norman - who has led opposition to the appointment - said disquiet over the job raised wider questions about how the Commons governed itself.
"This debate arises because of a widespread concern among colleagues across the House that the appointment process for the next clerk of this House was seriously flawed," he said.
Mr Norman said the new committee - which will report early next year - would examine the question of whether the procedural and management roles of the Clerk should be divided between different officials.
Mr Bercow, who headed the panel which originally chose Ms Mills but was not in the chair for Wednesday's debate, has said the proposal has merit and should be considered by MPs.
Confirming his involvement, Mr Straw said the committee would look into the case for separating the roles and how that might work in practice and make a series of recommendations.
However, he expressed concern that the committee was having to complete its work in nine weeks.
Ex-Commons leader Andrew Lansley - who sat on the original selection panel - said he believed the appointment was mistaken and accused Mr Bercow of seeking to "water down" the requirement in the job description that the Clerk should have "detailed knowledge of the procedures and practices of the House".
He said he believed the entire appointment process should be abandoned and a clerk appointed on a temporary basis until the House reached agreement on the future of the role.
But Labour MP Barry Sheerman said critics of the appointment had a "secret agenda", which amounted to wanting to "have a go at the Speaker".
And Tory MP Philip Davies said colleagues of his who were using the row as a "Trojan Horse for a personal vendetta" against Mr Bercow looked "absolutely ridiculous".
For the government, deputy Commons leader Tom Brake said it was "entirely proper" for the committee to look into the matter, saying the terms of the review was an issue for MPs, not ministers.
But he said it was important that it should be done in a "timely manner" and that the public should know which Commons officials were accountable for the "substantial challenges" the House faced.
Former Labour minister Jack Straw is to chair an inquiry into the governance of the House of Commons amid a row over the hiring of a new Commons Clerk.