Prince William and Kate Middleton, the Duke and Duchess of Cambridge, have celebrated 10 years of marriage with a video of the couple and their children enjoying the countryside.

William, the Queen’s grandson and second in line to the British throne, married Kate on April 29, 2011, in Westminster Abbey in a ceremony watched by millions around the world.

On Thursday, they posted a video showing the couple exploring a beach near their Norfolk home and roasting marshmallows with their children Prince George, seven, Princess Charlotte, five, and Prince Louis, three.

“Thank you to everyone for the kind messages on our wedding anniversary,” William and Kate said in a tweet.

“We are enormously grateful for the 10 years of support we have received in our lives as a family.”

A joyful Kate and William with two of their children in a clip from the anniversary video.

The duke and duchess also released two new photos on Thursday to commemorate the occasion.

Other members of the royal family, including the Queen, publicly congratulated the Cambridges on their milestone.

“Wishing the Duke and Duchess of Cambridge a very happy wedding anniversary,” the Queen’s official Twitter account wrote on a post of one of the new photos on Thursday.

“Today marks 10 years since their Royal Highnesses exchanged vows at Westminster Abbey.”

Prince Charles, William’s father, also offered good wishes through his social media channels.

William’s brother Prince Harry and wife Meghan Markle have reportedly also been in touch. A spokesman for the Duke and Duchess of Sussex confirmed “private congratulations” had been offered to the Cambridges, although it is not known if the two couples have actually spoken.

William and Harry have seen each other only once in more than a year – when the Duke of Sussex returned briefly from his Los Angeles home to attend the funeral of their grandfather, Prince Philip, at Windsor Castle on April 17.

Prince Harry was in Britain for less than 10 days, before returning to California to his pregnant wife and son Archie.

Prince Philip died on April 9 at the age of 99.

The Queen has recently returned to public duties, following an official mourning period for her husband of more than 70 years. She conducted audiences with a host of Commonwealth dignitaries this week – speaking to them via videolink from Windsor Castle.

-with AAP