Image copyright PA Image caption The Duke and Duchess of Cambridge say they feel "lucky" to have introduced their royal children to Canada

The Duke and Duchess of Cambridge have praised Canada for leaving their family with "happy memories" as their tour of Canada came to an end.

Prince William said they felt "very lucky" to have introduced Prince George and Princess Charlotte to the Commonwealth country.

The royal children stole the limelight during a trip to an outdoor fun day as part of the eight-day engagement.

The visit was their first official overseas trip as a family of four.

In pictures: Royals on Canada tour

Image copyright BBC NEWS Image caption Prince George was given ear defenders as the family flew out of Victoria in a seaplane

Image copyright Reuters Image caption The royal children stole the limelight during a trip to an outdoor fun day

Prince William said he and Kate were "incredibly grateful" to the people of Canada for the warmth and hospitality they had experienced as a family.

He added: "We have loved our time in British Columbia and Yukon and will never forget the beautiful places we have seen and the many people who have been kind enough to come to welcome us in person.

"We feel very lucky to have been able to introduce George and Charlotte to Canada. This country will play a big part in the lives of our children and we have created such happy memories for our family during this visit.

"Canada is a country of optimism, generosity and unrivalled natural beauty. I hope we have helped all Canadians celebrate what makes this country great. We will see you again soon."

Image copyright PA Image caption Prince William said the Commonwealth country would play a "big part" in the lives of his children

Image copyright Getty Images Image caption The trip had "created such happy memories for our family", Prince William said

Analysis, by diplomatic and royal correspondent, Peter Hunt, travelling with the Cambridges

For eight days, an important aspect of Canada's future has been on display. It's a future the majority of Canadians appear happy to embrace, for now.

The Cambridges have only visited parts of the country where people have applauded them coming, not questioned their existence.

They know the monarchy needs to be seen and appreciated to survive.

The public presence, at strategic points during the tour, of Prince George and Princess Charlotte will have bolstered, at the very least temporarily, the survival of this ancient institution.

Of course, what has been left unsaid this week is that Prince William and Prince George are not next in line. Prince Charles is waiting in the wings and his appeal in Canada is not as great as that of his son or his grandson.

Monarchists argue that's down to the allure of youth. Those seeking an elected, Canadian-born head of state see a chink in the armoury of the House of Windsor.

The couple visited parts of the Yukon and British Columbia which included a trip to the archipelago of Haida Gwaii and the gold rush town of Whitehorse.

Prince George and Princess Charlotte made a rare joint appearance at an official event with a play day with children of the Canadian military on Thursday.

Charlotte, 16 months, was heard speaking in public for the first time - saying "pop" at the balloons that filled Government House in Victoria.

The residence was transformed into a children's paradise, which included a petting zoo and miniature ponies.

Image copyright Reuters Image caption Prince George and Princess Charlotte made a rare joint public appearance during the trip to Canada

As part of the eight-day trip, the duke and duchess visited a charity in Vancouver which helps vulnerable mothers overcoming addiction and met refugees at an immigration centre.

The couple travelled in style, including taking a trip on a sea plane, and they also rowed a 25ft canoe.

They began their final day of the tour by visiting the Cridge Centre for the Family - one of Victoria's most well known charitable institutions.

The centre provides a range of services, including childcare, youth outreach and support for women who have experienced domestic violence.

Image copyright Getty Images Image caption Prince William and Kate were presented with personalised sports shirts for Prince George and Princess Charlotte

Their royal trip has been marked with a 100,000 Canadian dollar (£60,000) donation to benefit indigenous communities and refugees from the Canadian government.

Canadian Prime Minister Justin Trudeau announced the money would be divided equally between the Prince's Charities Canada (PCC) and the Immigrant Services Society of British Columbia (ISSofBC).

Mr Trudeau said: "In keeping with tradition, I am honoured to mark the visit by the Duke and Duchess of Cambridge with a gift that will help both indigenous youth as well as newcomers to Canada realise their dreams.

"Canadians have a real affection for the Royal Family which was once again very much on display during this tour."