The Conservative premier offered Britain's deepest gratitude and good wishes to the 95-year-old as he stands down from public engagements.
"From his steadfast support for Her Majesty the Queen to his inspirational Duke of Edinburgh Awards and his patronage of hundreds of charities and good causes, his contribution to our United Kingdom, the Commonwealth and the wider world will be of huge benefit to us all for years to come," May said.
The Duke's retirement was revealed when the Queen's most senior aides were ordered to attend a special meeting at the palace in London – led by William Peel, the Lord Chamberlain. Staff were told that Philip would be retiring in September.
Labour leader Jeremy Corbyn said the monarch had dedicated his life to supporting The Queen and the UK. "His Duke of Edinburgh's Award scheme has inspired young people for more than 60 years in over 140 nations," the republican said. "We thank Prince Philip for his service to the country and wish him all the best in his well-earned retirement."
Ukip leader Paul Nuttall urged people to honour the Duke's public service. "For over 60 years he has been a dedicated public servant, and deserves our great thanks. Happy retirement Sir," he said.
But not all reactions to Philip's retirement news were flattering. Graham Smith, chief executive of campaign group Republic, said: "Philip himself admitted he had nothing to do with [the Duke of Edinburgh] Award scheme. Let's all stop the toadying."
Full Buckingham Palace statement
His Royal Highness The Duke of Edinburgh has decided that he will no longer carry out public engagements from the autumn of this year. In taking this decision, The Duke has the full support of The Queen.
Prince Philip will attend previously scheduled engagements between now and August, both individually and accompanying The Queen. Thereafter, The Duke will not be accepting new invitations for visits and engagements, although he may still choose to attend certain public events from time to time.
The Duke of Edinburgh is Patron, President or a member of over 780 organisations, with which he will continue to be associated, although he will no longer play an active role by attending engagements.
Her Majesty will continue to carry out a full programme of official engagements with the support of members of the Royal Family.