The Duke of Cambridge has paid tribute to Australia, describing the nation as a "magnet" for investors, visitors and those wanting a better quality of life.

As the Cambridges' tour down under draws to a close William praised his hosts' legendary sporting prowess, flourishing arts and the important role they played on the world stage.

William and Kate will stand shoulder to shoulder with Australians tomorrow when they join events marking Anzac day - a national day of remembrance for the nation's war dead, veterans and those still serving.

The Duke said he, his wife and brother Prince Harry would be taking part in events next year commemorating the centenary of the First World War's Gallipoli campaign that featured Australian troops.

Speaking at a reception hosted by prime minister Tony Abbott at Parliament House in Canberra, William told the guests who included leading figures: "Australia has a quality of life and a level of excellence that makes it a magnet: an enormously attractive place to live, trade, invest, and indeed just visit.

"The arts and sciences flourish; Australian sporting success is legendary; agriculture - from the traditional to the technologically most advanced - is hugely successful. This is a country that is in the front rank internationally.

"We have both seen all this for ourselves. Australia may be known as 'the Lucky Country', but often the harder you work, the luckier you get. Australians make their own luck.

"The distinct Aussie formula that has fashioned such a dynamic society is the source of admiration and envy around the world."

William and Kate have spent more than a week visiting Sydney, Brisbane, Adelaide, and the iconic landmark of Uluru.

The Duke added: "There is so much to admire about Australia. Catherine and I acknowledge the timeless values of the Aboriginal and Torres Strait Islander peoples.

"They have been the custodians of this ancient and majestic continent for thousands of years. The traditional owners' stories, and the magnificent and moving rock art at Uluru, which we saw for ourselves, are a priceless inheritance. They tell us not just about the past but provide a precious vision for the future."

Meanwhile the couple have sympathised with the Duchess of Cornwall after her brother died following a fall.

William and Kate expressed their sadness after hearing about the death of Mark Shand, who died yesterday from a serious head injury sustained in a fall in New York.

Mr Shand, 62, was taken to hospital on Tuesday night after reportedly slipping while lighting a cigarette and hitting his head on the pavement outside an after-party for a charity event.

Kensington Palace said: "The Duke and Duchess of Cambridge were saddened to learn this morning of the tragic death of Mark Shand.

"Their thoughts are with the Duchess of Cornwall and her family at this time."

The Australian premier also gave a speech and joked about Prince George, describing the moment when the royal baby returns to the country as King George VII.

Speaking about William's previous visit in 2011 and the present tour, Mr Abbott told him: "We have seen in you, sir, during both your visits, through your words and through your deeds, the decency and the sense of duty of your father and the compassion of your mother."

He added: "Your grandmother, the Queen, opened this building in 1988. And your father, the Prince of Wales, has been here many, many times.

"Many decades, hence, when a currently unknowable Australian prime minister welcomes your son, King George VII, to this building, that will be a sign of the stability and the continuity in the life of our nation."

After the reception was entertained by award-winning indigenous Australian singer Geoffrey Gurrumul Yunupingu, the royal couple mingled with the 600 guests, who included leading musicians, Olympic athletes, fashion designers, decorated war heroes and politicians.

William joked with guests that, during his visit to Sydney's Manly Beach last week, he had wanted to tear off his trousers and reveal a pair of swimming trunks.

Vicki Kelly, wife of MP Craig Kelly, said: "Prince William said he was hoping to rip off his pants with Velcro down at the beach with Tony Abbott to reveal their Speedos."

Mr Kelly said: "This tour shows the Royal Family actually has a human face. Sometimes, it often seems to Australians that it is a lofty concept but the way they are here is different."

Television presenter Paul Murray, who has a show called Paul Murray Live, asked William what had been his favourite part of the tour.

Mr Murray said: "William replied that it was the Blue Mountains. He also said Manly Beach was very beautiful and he acknowledged the visit he made to the hospice in Manly, too.

"I told him that we would name a state after Prince George if they agreed to stay longer but he just laughed and said 'No, that's OK'."

Former INXS guitarist Kirk Pengilly, 55, was also a guest, along with his wife, professional surfer Layne Beachley, 41.

He said "It's great to be here today. The royal couple have done so much for Australia during this visit.

"I met Charles and Diana in 1985 at a show with other Australian groups.

"When we met them in the line-up, Charles said to Andrew (Farriss, the band's keyboardist), who is one of our more shy members, 'You must be quite shagged after that'. Shagged means something quite different in Australia and we all had a big chuckle about that. It was quite funny."

The royal couple's day began with a visit to the new national arboretum in Canberra, where they spoke to children about conservation projects.

Kate confessed she was sweltering in her bright green Catherine Walker coat-dress as she toured the attraction.

The Australian capital was bathed in warm sunshine as the Duchess chatted to well-wisher Karen Vey, 39, who said: "She said we were very lucky to have this beautiful weather. I said 'I'm quite hot'. She said she was very hot and I said 'You would be in that outfit'."

Following the devastating 2003 bushfires in Canberra, the Australian Capital Territory Government dedicated an area of burnt-out pine forest west of the city as the site for an innovative new national arboretum.

A national design competition was held for the new arboretum and in 2005 the winners were announced - Taylor Cullity Lethlean Landscape Architects and Tonkin Zulaikha Greer Architects with their "100 forests and 100 gardens'' joint proposal.

William and Kate also visited the National Portrait Gallery and met leading Australians who had been depicted on canvas or in bronze.

In the evening, Governor-General Sir Peter Cosgrove hosted a drinks reception for the couple at his official residence, Government House, where the Duke and Duchess are staying with baby George.

Kate looked stylish in a Lela Rose cocktail dress and stood with her husband as the Governor-General gave a speech in honour of his guests.

Sir Peter highlighted the parallels between the Cambridges' trip and the 1927 tour of Australia by William's great-grandparents, the Duke and Duchess of York, later George VI and Queen Elizabeth.

He said they were also young parents to 13-month-old Princess Elizabeth, now the Queen and William's grandmother.

The Governor General added: "Accounts of their visit note the deafening cheers of the crowds, the fervent and spontaneous greetings of those they met, and the Duchess won hearts from the start - all words that could describe the last couple of weeks."

Around 100 guests filled the drawing room at Government House, all people who have made outstanding contributions in a range of areas from the arts, to business, the charitable sector, conservation, the military and sport.

Among those invited was Victoria Cross recipient Corporal Ben Roberts-Smith - Australia's most decorated modern soldier.

The serviceman, who announced last year that he was leaving the army, was awarded the highest honour for bravery in the face of the enemy in 2011 for his role assaulting enemy machine gun positions in Afghanistan while the rest of his squad was pinned down.