In the closing stages of the Second World War Morris served in the 9th Queen's Royal Lancers, and in 1945 was posted to the Free Territory of Trieste, during the joint Anglo-American occupation.

In 1949, Morris married Elizabeth Tuckniss, the daughter of a tea planter; they had five children together, including the poet and musician Twm Morys. One of their children died in infancy.

After the war Morris wrote for The Times, and in 1953 was its correspondent accompanying the British Mount Everest Expedition, which in the event was the first to scale Mount Everest. Morris reported the success of Hillary and Tenzing in a coded message to the newspaper, "Snow conditions bad stop advanced base abandoned yesterday stop awaiting improvement", and by happy coincidence the news was released on the morning of Queen Elizabeth's coronation.

Reporting from Cyprus on the Suez Crisis for The Manchester Guardian in 1956, Morris produced the first "irrefutable proof" of collusion between France and Israel in the invasion of Egyptian territory, interviewing French Air Force pilots who confirmed that they had been in action in support of Israeli forces.

Morris has received honorary doctorates from the University of Wales and the University of Glamorgan, is an honorary fellow of Christ Church, Oxford, and is a fellow of the Royal Society of Literature. She received the Glyndŵr Award for Outstanding Contribution to the Arts in Wales in 1996.

She accepted her CBE in the 1999 Queen's Birthday Honours "out of polite respect", but is a Welsh nationalist republican at heart. In 2005, she was awarded the Golden PEN Award by English PEN for "a Lifetime's Distinguished Service to Literature". In January 2008, The Times named her the 15th greatest British Writer since the War. She has featured in the Pinc List of leading Welsh LGBT figures.

Morris began medical transition in 1964. In 1972, Morris travelled to Morocco to undergo sex reassignment surgery, performed by surgeon Georges Burou, because doctors in Britain refused to allow the procedure unless Morris and Tuckniss divorced, something Morris was not prepared to do at the time. They divorced later, but remained together and on 14 May 2008 were legally reunited when they formally entered into a civil partnership. Morris detailed her transition in Conundrum (1974), her first book under her new name, and one of the first autobiographies to discuss a personal gender reassignment. The opening lines of Conundrum have since become famous “I was three or perhaps four years old when I realized that I have been born into the wrong body, and should really be a girl. I remember the moment well, and it is the earliest memory of my life.”

In an interview with BBC in 2016 she told Michael Palin that she does not like to be described as a travel Writer, as her books are not about movement and journeys; they are about places and people.