The committee will shadow David Davis' new Department for Exiting the European Union, and provide cross-party oversight of the government's most significant body of work over the next few years.
Labour's party leadership formally supported remaining within the European Union, although some of its MPs, most notably Gisela Stuart, who chaired the official Vote Leave campaign.
Select committee roles have become increasingly important to Labour MPs who do not back the party's current leadership, with many former shadow cabinet members taking spots on committees.
Brexit committee: How it works
Now that party whips have agreed which party should lead each committee, select committee chairs will be elected in a vote of all MPs, currently set for 19 October.
In addition to the Brexit watchdog, Labour will additionally retain ownership of the new Business, Energy and Industrial Strategy Committee.
The new BEIS unit will be created from a merger of the SNP led Energy and Climate Change and Labour-led Business Innovation and Skill committees.
The news will come as a blow to ECC chair Angus MacNeill, who had hoped to lead the new committee.
As a result of losing the ECC committee, the SNP will gain the consolation prize of leading a new committee giving oversight to Liam Fox's department for international trade.