Ms Cooper, a former cabinet minister and the current chairwoman of the Commons Home Affairs Committee, becomes shadow home secretary and will take on Priti Patel over the migrant crisis.
Sir Keir also handed big promotions to two of Labour’s rising stars, Bridget Phillipson and Wes Streeting, who take on the roles of shadow education secretary and shadow health secretary.
Jonathan Ashworth who has had the health brief through the pandemic, is moved to shadow work and pensions secretary.
A warm welcome to the new Shadow Cabinet team and a heartfelt thank you to those who have left.
The Labour Party I lead is focused on the priorities of our country and holding the Conservative Government to account.
With Labour, Britain’s best days are ahead. pic.twitter.com/isHyfTqH9h
— Keir Starmer (@Keir_Starmer) November 29, 2021
In other moves, Lisa Nandy will face off against Michael Gove as shadow secretary for levelling up and communities. She will be replaced as shadow foreign secretary by David Lammy.
Former leader Ed Miliband becomes shadow climate change secretary, while Jonathan Reynolds takes on his former portfolio of business, energy and industrial strategy.
“With this reshuffle we are a smaller, more focused shadow cabinet that mirrors the shape of the Government we are shadowing,” Sir Keir said.
“We must hold the Conservative Government to account on behalf of the public and demonstrate that we are the right choice to form the next government.”
Earlier it appeared the reshuffle would be overshadowed as tensions resurfaced between Sir Keir and his deputy, Angela Rayner.
I don’t know the details of the reshuffle or the timing of it
Ms Rayner appeared to be blindsided when news of the reshuffle broke, as she was delivering a keynote speech on Labour’s plans for reforming standards in public life.
“I don’t know the details of the reshuffle or the timing of it,” she said in response to reporters’ questions.
“I’ve been here concentrating on my role now, but six months ago I said again, we need some consistency in how we’re approaching things as an opposition.”
A spokesman for Ms Rayner later said the leader and his deputy had spoken between her morning round of media interviews and her speech at the Institute for Government (IfG).
Nick Thomas-Symonds, who was shadow home secretary, takes on international trade in what is ostensibly a demotion.
Looking forward to getting to work as @UKLabour Shadow Home Secretary, working with @Keir_Starmer & building on the work done by @NickTorfaen.
We want our communities & country to be strong, safe & secure. The Home Office is badly letting people down. Much to do.
— Yvette Cooper (@YvetteCooperMP) November 29, 2021
However Sir Keir softened the blow by announcing that he had asked him to head a new shadow cabinet committee leading the party’s response on Brexit.
Elsewhere, Lucy Powell becomes shadow culture secretary, Jim McMahon gets environment, Louise Haigh goes to transport and Steve Reed gets justice.
The veteran former minister Pat McFadden becomes shadow treasury chief secretary while former leadership contender Emily Thornberry is the shadow attorney general.
Peter Kyle enters the shadow cabinet as shadow Northern Ireland secretary while Jo Stevens becomes shadow Welsh secretary.
Those leaving include the former shadow education secretary Kate Green, the former shadow environment secretary Luke Pollard and the Blair-era veteran Lord Falconer, who announced he was stepping down as shadow attorney general.
It’s been an honour to serve on the Labour front bench since 2015 but I’m looking forward to spending even more time at home here in Lancashire and standing up for my constituents. pic.twitter.com/8pybEql5WB
— Cat Smith MP (@CatSmithMP) November 29, 2021
Earlier, Cat Smith, who was shadow minister for young people and one of the last acolytes of Jeremy Corbyn on the Labour frontbench, announced she was quitting, citing the continued withholding of the Labour whip from the former leader.
“This position is utterly unsustainable and it is important that you truly understand how much damage this is causing in constituency Labour parties and amongst ordinary members, a number of whom are no longer campaigning.” she wrote in her letter of resignation.
Shadow chancellor Rachel Reeves, party chair Anneliese Dodds and shadow defence secretary John Healey are among those remaining in their current posts.
In a statement, Sir Keir said: “I want to thank all those who have left the shadow cabinet today for their great service to me and to our party.
“I look forward to working with the new team to show we are once again a serious party of Government, ready to fix the mess the Tories have got the country into and to inspire voters to believe that Britain’s best days are ahead of us.”