The announcement came as the couple arrived in Sydney at the start of a 16-day visit to Australia, Fiji, Tonga and New Zealand.

The trip is their only international tour since the Duke and Duchess of Sussex were married in May, apart from a two-day visit to Ireland.

The palace said the couple has “appreciated all of the support they have received from people around the world since their wedding in May and are delighted to be able to share this happy news with the public”.

The Queen, the Duke of Edinburgh, the Prince of Wales, the Duchess of Cornwall and the Duke and Duchess of Cambridge were said to be “delighted” for the couple.

Doria Ragland, the duchess’s mother, said she was “very happy about this lovely news” and “looks forward to welcoming her first grandchild”.

The British prime minister, Theresa May, said: “My warmest congratulations to the Duke and Duchess of Sussex on the happy news they are expecting a baby in the spring. Wishing them all the best.”

The duchess once described motherhood as being on her “bucket list”, while her husband has often spoken of his desire to have children.

In Sydney, holding hands and casually dressed, the 34-year-old prince and the former American actress walked out an airport rear entrance and into a car. Meghan, 37, wearing skinny black pants and a black, burgundy trimmed coat, was smiling and clutching folders, while Harry gave a thumbs up to bystanders.

Days after watching Harry’s cousin Princess Eugenie tie the knot in a lavish ceremony in Windsor, the couple touched down in Sydney on an overcast morning after a regular Qantas Airways flight from London with a brief stopover in Singapore.

Following the announcement that the royal couple is expecting a baby, Australian Prime Minister Scott Morrison, who plans to climb with Harry to the top of the Sydney Harbour Bridge, tweeted: “What fantastic news! Australia is thrilled for you both. Looking forward to sharing in the joy during your stay down under.”

The big announcement came with the nation gloomily pondering the prospects of Britain crashing out of the European Union without an agreement, after frenzied negotiations hit a weekend roadblock.

Television stations broke away from their Brexit coverage, banner headlines appeared on newspaper websites, and debates began about possible name for the future seventh in line to the British throne.

Google said searches for “when is spring?” had spiked while United Kingdom newspapers played up an inter-continental rivalry over what the child, who will become either an earl or a lady, will be called.

Meghan was a popular United States actress before becoming the Duchess of Sussex. Some UK media said the California native would draw on her American roots.

But the bookies are favouring Diana – name of the late princess who was mother to both Prince Harry and his older brother Prince William – along with Arthur and Alice.

Meghan made her name in acting as a savvy para-legal Rachel Zane in the US television legal drama Suits.

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In her first solo charity project, she launched a cookbook in September in support of families affected by the Grenfell Tower fire disaster in London.

The duchess wrote the foreword to the recipe collection entitled Together: Our Community Cookbook, produced by women who suffered in the fatal blaze.

The June 2017 fire in a 24-storey residential block killed 71 people and left many more living in temporary accommodation.

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Meghan’s every smile, step and wave has been scrutinised by royalty watchers curious to see how the mixed-race star will perform in her new role.

She is adored by the public and shadowed at every appearance by the press, with dozens of UK reporters following the couple to the Pacific.

British media last month got particularly excited about her closing her own car door at her first solo engagement – the opening of an exhibition at the Royal Academy of Arts in London.

The gesture was interpreted as a sign that Meghan remained a down-to-earth woman without pretences, a princess of the people.

Harry and Meghan had said during an earlier television interview that they wanted to promote humanitarian causes close to their hearts across Commonwealth-member countries, including Australia.

The royal couple’s visit comes six months after Harry’s father, Prince Charles, made his 16th official visit to Australia, primarily to open the 21st Commonwealth Games at Gold Coast city in Queensland

– With additional reporting from The Guardian and agencies