William and Kate shared a tweet addressed to the leader on Tuesday, saying her friendship had been valuable particularly following the Queen’s death last year.
Writing on their official Kensington Royal account, they also expressed “best wishes” for Ms Ardern’s partner, television presenter Clarke Gayford, and her four-year-old daughter Neve.
The royal couple said: “Thank you @jacindaardern for your friendship, leadership and support over the years, not least at the time of my grandmother’s death.
“Sending you, Clarke and Neve our best wishes. W & C.”
Ms Ardern was among the world leaders at the Queen’s funeral at Westminster Abbey on September 19.
Two months before the Queen died, William had welcomed Ms Ardern to Kensington Palace during her first trip to the UK since the coronavirus pandemic.
Their meeting was held in private, but a spokesman for William, who was then the Duke of Cambridge, said it took place on July 2.
In April 2019, William visited New Zealand to pay tribute to those affected by the Christchurch terror attack, in which 50 people were killed.
He met survivors of the attack and their families, members of the emergency services and Muslim community leaders.
Ms Ardern has also previously spoken of a “real connection” with the royal family following separate visits to her homeland by William and Kate, and the Duke and Duchess of Sussex.
The New Zealand Labour Party politician dramatically resigned last week, saying she no longer had “enough in the tank” to fulfil the demanding role.
Over the weekend her Labour Party colleagues voted unanimously Sunday for Chris Hipkins to take over as prime minister, and he will be sworn in on Wednesday.