text: "Welcome to Canada - honeymoon capital of the Commonwealth," David Johnston said before crowds at Government House.
  Prince William, who began his address in French, Canada's official language alongside English, said he and his wife had had a "longing" to visit together.
  The duke and duchess earlier visited Canada's National War Memorial.
  The couple will be staying at Government House - also known as Rideau Hall - while in Ottawa.
  Prime Minister Stephen Harper spoke after the governor general, saying: "Your journey across our fair Dominion marks the beginning of your journey into the hearts of Canadians. We wish you all the best on both counts.
  "We are both honoured and delighted that you have chosen us for your first official tour together."
  Prince William responded: "Merci beaucoup, Votre Excellence et Monsieur le Premier Ministre, pour votre accueil chaleureux."
  This was translated live on Canadian television as: "Thank you very much Your Excellency and Prime Minister for your warm welcome."
  The duke continued: "Catherine and I are so delighted to be here in Canada.
  By Peter HuntBBC royal correspondent
  They are the British and, indeed, the Canadian monarchy's future.
  The enthusiastic, large crowds were keen to catch a glimpse of their future king and queen - this in a country where, according to a recent opinion poll, almost half of its citizens think the monarchy "is a relic of a colonial past that has no place in Canada today".
  The dissenters weren't in evidence today. The streets were filled by the dedicated and the curious.
  They saw a much talked about "fresh and modern" royal couple carry out a tried and tested programme of engagements, including a speech by Prince William in English and French.
  He'll be partially bilingual for the next nine days as he tours a country which has had both French and British monarchs.
  More from Peter Hunt
  "Instilled in us by our parents and grandparents, who love this country, we have been looking forward to this moment for a very long time - and before we were married, we both had a longing to come here together.
  "The geography of Canada is unsurpassed and is famous for being matched only by the hospitality of its people."
  Switching to French again, Prince William joked: "It will improve as we go along."
  The royal couple later attended a barbecue hosted by Mr Johnston, who acts as the Queen's official representative in Canada.
  Canada is a member of the Commonwealth and Queen Elizabeth II, Prince William's grandmother, is its head of state.
  At the war memorial earlier, Prince William laid a wreath and his wife Kate placed a bouquet of flowers. They split up to greet some 3,000 well-wishers.
  Before their walkabout fans could be heard chanting: "We love you Kate", but there were also screams for the duke.
  Alexandra Anghel, 18, from Ottawa waited five hours to see the royal couple. She said the duchess seemed "down to earth".
  "It was a surreal moment to meet her, someone I never thought I would ever meet and there she was in front of me. William's lineage is amazing, he's literally walking history - I can't believe I saw walking history."
  The duke and duchess, who married in April, will visit seven Canadian cities on their nine-day visit, before heading to the US.
  On Friday, they will celebrate Canada's national day. The pair will also visit Quebec, Prince Edward Island, where they are to participate in a dragon boat race, and Calgary.
  In Calgary they will open the Calgary Stampede - an annual rodeo and festival dubbed the "greatest outdoor show on Earth".
  Canada has created a new royal flag for the visit, which features three maple leaves, from Canada's national tree, at its base.
  The flag flew from the cockpit of the jet carrying the royal couple when it touched down from the UK on Thursday afternoon local time. It will also fly from their cars and buildings they are visiting or staying in.
  Map of tour highlights
  The visit will be closely followed by the media, with nearly 1,400 journalists - including about 100 from Britain - accredited to cover the visit.
  The Duchess of Cambridge has reportedly packed up to 40 different outfits for the tour.
  She left London wearing a dress by French designer Roland Mouret and a blazer by Canadian label Smythe les Vestes and changed into a navy lace dress by Erdem Moralioglu during the flight to Ottawa.
  Mosha Lundstrom Halbert, associate fashion news editor at Canadian fashion magazine Flare, said Kate's choice of clothing was symbolic.
  "It's very exciting," she said. "To me, Erdem really represents the crossover between British and Canada fashion. He's really established in the UK but Canada is where he was born and raised."
  BBC royal correspondent Peter Hunt says Canada is a safe first visit for a royal spreading her new wings, while US residents continue to be fascinated by Britain's royalty.
  The cost of the visit to the Canadian government, not including security, is estimated to be 1.4 million Canadian dollars (Â£958,580).
  A poll commissioned by the Toronto Star newspaper found that more than half the 18 to 34 year-olds questioned about the visit were indifferent about the trip.
  The duke and duchess will travel to the US state of California for two days from 8 July, attending a black-tie Bafta reception and dinner in Los Angeles on 9 July. Prince William is Bafta's president.
target: Canada's governor general has welcomed the Duke and Duchess of Cambridge to Ottawa at the start of the royal couple's first official overseas tour.