The executive chairman of the supermarket and former Tory donor said Sir Keir has “transformed” Labour since taking over from Jeremy Corbyn four years ago.
And Mr Walker praised the Labour leader’s “compassion and concern for the less fortunate”, which he said contrasts with the Conservatives under Mr Sunak.
Writing in The Guardian, he said: “Labour is the right choice for the communities across the country where Iceland operates – and the right choice for everyone in business who wants to see this country grow and prosper.”
Mr Walker said that when he quit the Conservative Party in October, he had not committed to supporting Labour. And he acknowledged criticism of the party under Sir Keir, that voters “don’t yet know him well enough” to be enthused about the prospect of a Labour government.
But he added: “Having met the man, I am sure that Starmer has exactly what it takes to be a great leader.”
“He absolutely gets it when I talk to him about the way that the cost of living crisis has put unbearable strain on the finances of so many of my customers and their families, and the urgent need for a government that does everything in its power to ease their burden,” Mr Walker said.
He also heaped praise on shadow chancellor Rachel Reeves, who he said “understands the critical importance of wealth creation” and “knows that we must revive our manufacturing and services”.
Mr Walker went on to say the country is “in a mess” and accused the Conservatives of having “failed the nation”.
He told BBC Breakfast: “I think the Conservatives have failed the nation. They’ve drifted badly out of touch with people like my customers, and they’re drifting further and further to the right.
“What’s interesting is that my values and principles haven’t changed, and, whilst the Conservatives have moved away from me, Labour has steadily moved towards the centrist pragmatic views that I’ve long held.”
He said Labour is “on the right track and the right party”.
“The country is in a mess, the country is in a significantly worse place than it was 14 years ago.”
But Mr Walker said he does not agree with “every single thing that Labour proposes”. And he said he is not joining the party, so he can speak out “without fear or favour about the issues that matter to me and the people my business employs and serves”.
Mr Walker’s backing for Sir Keir is the latest blow for Mr Sunak and the Conservatives as business leaders flock to Labour ahead of the next general election.
It comes after former Bank of England governor Mark Carney backed the party and Conservative grandee Kenneth Clarke praised Ms Reeves for her work as shadow chancellor.
And it follows the advertising giant that helped to put Margaret Thatcher in power, Saatchi & Saatchi, attacking the “cruelty” of the Conservatives and backing Labour to win the next election, expected this autumn.
Mr Walker’s support for the party is also a major about-turn for the grocery chief, who until quitting the Tories wanted to stand as a candidate for the party in the election.
At the time, he attacked the Tories for “flip-flopping” on net zero and HS2 and said his views on food bank usage and sewage were “unwelcome” in the party.
“I was told to pipe down. I am not willing to wear a gag to bag a seat and I am not willing to change my values and principles to suit a party that itself has lost its way,” he said.