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The Canadian premier is in Europe ahead of a key G20 summit in Hamburg, Germany later in the week.
On the second of a three-day visit to the Republic of Ireland, Mr Trudeau will also meet President Michael D Higgins at his official residence.
Trade issues are set to dominate the agenda, with the Canada-EU free trade deal expected to be a focal point.
Trade unions, farmers and environmental groups are concerned about the deal.
It proposes a significant reduction of trade tariffs between the EU and Canada, and officials hope it will generate an increase in trade worth $12bn (€10.9bn; £9.8bn) a year.
The European Parliament needs the approval of member states' national parliaments before the trade deal can fully come into effect.
Mr Trudeau arrived in Dublin with his wife, Sophie Grégoire, and their youngest son, Hadrien, on Monday.
The Canadian prime minister will attend a business lunch and visit famine memorial statues in the city centre before a state dinner hosted by the Taoiseach.
The visit was arranged in May when Mr Varadkar's predecessor Enda Kenny met the Canadian leader in Montreal.