Trump's repeated suggestion that the US annex Canada prompted Prime Minister Carney to invite Charles to give the speech from the throne.
The King is the head of state in Canada, which is a member of the British Commonwealth of former colonies.
Carney said in a statement the visit spoke to the "vitality of our constitutional monarchy and our distinct identity".
It is rare for the monarch to deliver what's called the speech from the throne in Canada.
Charles' mother, Queen Elizabeth II, did it twice in her 70-year reign, the last time in 1977.
The speech is not written by the king or his UK advisers as Charles serves as a nonpartisan head of state.
He will read on Tuesday what is put before him by Canada's government.
Carney, the new prime minister and a former head of the Bank of England, and Canada's first Indigenous governor-general, Mary Simon, the King's representative in Canada, met the King on Monday.
Canadians are largely indifferent to the monarchy, but Carney has been eager to show the differences between Canada and the United States.
The King's visit clearly underscored Canada's sovereignty, he said.
Carney won the job of prime minister by promising to confront the increased aggression shown by Trump.
The new US ambassador to Canada, Pete Hoekstra, said sending messages to the US is not necessary and Canadians should move on from the 51st state talk, telling the Canadian Broadcasting Corporation that if there's a message to be sent there are easier ways to do that, such as calling him or calling the president.
A horse-drawn carriage will take the king and queen to the Senate of Canada Building for the speech.
It will accompanied by 28 horses - 14 before and 14 after.
He will receive the Royal Salute from the 100-person guard of honour from the 3rd Battalion, Royal Canadian Regiment before entering the chamber for his speech.
The King will return to the UK after the speech and a visit to Canada's National War Memorial.
