Justin Trudeau will have a private audience with the monarch at Holyroodhouse Palace.
It is in Europe before the G20 key summit in Germany after the week when it is expected that trade issues to dominate the agenda.
M. Trudeau met with Irish Prime Minister Leo Varadkar and President Michael D. Higgins in Dublin on Tuesday.
The visit comes as Canada celebrates the 150th anniversary of its various provinces in a single country.
M. Trudeau, 45, was elected second youngest minister in Canadian history two years ago.
Prior to the visit to Scotland, she said she wanted to honor the Queen’s commitment to public functions, which, she said, “inspired me a lot and many other Canadians.”
The Queen welcomed the annual Martes Festival Gardens at Holyroodhouse Palace
And he said he wanted to “recognize the strong family ties, history and common purpose shared by our countries.”
M. Trudeau has already met with the Queen at Buckingham Palace shortly after her election in 2015 with several children in the 1970s when her father Peter was the Prime Minister of Canada.
M. Trudeau is of Scottish descent, his grandfather William Sinclair was born in Banffshire before his family emigrated to Canada in 1911.
The Queen is located in Edinburgh for traditional events Holyrood Royal Family Week.
He met with Prime Minister Nicola Sturgeon and Ken Macintosh, the Speaker of the Scottish Parliament, in public hearings at the palace Tuesday.