"The panel will review the preparations and performances in the Rugby World Cup, the effectiveness of the coaching, management and support team and consider feedback from all relevant stakeholders," the Rugby Football Union (RFU) said in a statement on Monday.
England went out at the pool stage for the first time after home defeats by Wales and Australia and the panel will look at the future of coach Stuart Lancaster, who has a contract until 2020, and his assistants.
McGeechan, the hugely respected former British and Irish Lions coach and player, has been a vocal supporter of Lancaster during the tournament.
After Sam Burgess and Owen Farrell were controversially chosen for the Wales match, McGeechan said he "did not know what all the fuss is about" and described it as a "shrewd selection".
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He also wrote after England's exit that Lancaster should be retained. "I can't see anything better out there that is readily available," said the Scot.
England's 2003 World Cup-winning lock Kay is now a respected TV pundit and he will be joined on the panel by Ian Metcalfe, chairman of the Professional Game Board, and Ian Watmore, a board member of England's World Cup organising committee and former CEO of the Football Association.
"While the RFU will be focusing on continuing to deliver a fantastic tournament over the next two weeks, it is hugely disappointing not to have progressed through to the knockout stages," Ritchie said.
"With that in mind we have begun to review the senior team's campaign to ensure that we learn and improve from this experience in order to be consistently successful.
"There will be extensive input from players, coaches and management staff as well as an external perspective gathered. The details of this feedback will remain confidential with recommendations then made to the RFU board."
Four years ago the results of a confidential player feedback into the 2011 World Cup campaign were leaked to a newspaper.
(Editing by Tony Jimenez)
