Britain's Prince Harry and his wife Meghan are expecting their first baby in spring next year, Kensington Palace said on Monday.

"Their Royal Highnesses The Duke and Duchess of Sussex are very pleased to announce that The Duchess of Sussex is expecting a baby in the Spring of 2019," the couple's official residence wrote, using their royal titles.

Harry, 34, and Meghan, a 37-year-old former actress from the United States, married at Windsor Castle in England in May, in a star-studded service that was watched all over the world.

The announcement comes as the couple started their first major international tour together as royals, a 16-day trip that includes Australia, Fiji, Tonga and New Zealand.

Upon touching down in Sydney on Monday, the royal couple smiled and held hands as they made their way through a swarm of media at the airport. They are spending the day in private to recover from the long flight before official engagements start on Tuesday.

They include meeting political leaders for the official welcome, a pair of koalas, a boat ride on the harbour and a meet-the-people walk at Sydney Opera House.

The royal couple's main purpose is to open and attend the Invictus Games in Sydney, which open on Saturday and run through October 28.

The sporting event was founded by Prince Harry in 2014 for injured and disabled military veterans to engage in competitive events such as wheelchair basketball, athletics and swimming.

Sixth in line to the throne, Harry is the second son of Prince Charles and the late Princess Diana. His brother, Prince William, is second in line to the throne behind Charles.

Meghan has made several high-profile appearances in Britain since her marriage, including a trip in June with Queen Elizabeth II, Harry's grandmother, to open a landmark bridge and a regional theatre in north-western England.

The couple visited Ireland in July, their first trip abroad since getting married.