Mr Trudeau, whose father was also a Canadian prime minister, said he was “extraordinarily fortunate to have known Her Majesty throughout my life”.
“The first time I met her was in 1977 when I was just a little boy,” he told MPs during a special session of Canada’s House of Commons.
“When I would meet with her as Prime Minister almost four decades later in 2015, I joked that the last time that we had met she had been taller than me – she responded with a quip about my making her feel old.
“Her sense of humour was one of her many great qualities and one of the many reasons why she was one of my favourite people in the world.”
Mr Trudeau said for most Canadians she was “the only sovereign that most of us have ever known” and “her sudden absence has struck us all palpably and profoundly”.
The Queen “embraced her role” as Canada’s monarch and had felt at home in the country – particularly enjoying being able to speak her impeccable French, Mr Trudeau said.
“Her conversations with me were always candid, we talked about anything and everything, she gave her best advice on a range of issues, she was always curious, engaged and thoughtful,” he said.
Canadians “feel like they have lost a family member who grew up alongside us”.
The Canadian Prime Minister said: “The Queen had a profound appreciation for our culture.
“In 1964, she said that she was happy to know that there existed in our Commonwealth a place where it was expected of her that she would speak officially in French.
“It’s a language that she loved a lot and that she spoke impeccably well.”
Mr Trudeau said King Charles would carry on his mother’s legacy.
The then prince of Wales visited Canada in May, where he faced calls for a royal apology for the “assimilation and genocide” of Canada’s indigenous residential schoolchildren.
The prince did not make an admission on behalf of the monarch but instead “acknowledged” the nation’s dark past, First Nations leaders said after meeting the future king.
“Our new king, King Charles III, demonstrated his commitment to the larger sweep of history with his most recent tour that included a focus on the generational work necessary to achieve reconciliation and fight climate change,” Mr Trudeau told Canada’s MPs.
The Canadian Prime Minister also gave details about the delegation he will lead to the state funeral.
He will be accompanied by his wife Sophie Gregoire Trudeau and the delegation will also include governor general Mary Simon and former prime ministers and governors general.
Members of the Order of Canada including actress Sandra Oh, swimmer Mark Tewksbury and musician Gregory Charles will also attend.
The Royal Canadian Mounted Police and representatives of regiments of the Canadian Armed Forces will join uniformed personnel from other Commonwealth countries for the service on September 19.