The recommendation is part of a "bold long-term strategy" that the panel says is essential to realising economic and social benefits such as filling skills shortages and boosting trade and innovation.
As well as doubling the 239,000 international students Canada currently attracts - a feat the panel describes as "feasible" - International Education: A Key Driver of Canada's Future Prosperity also says that the country should send 50,000 domestic students abroad for study or cultural exchange by 2022.
It calls on the government to invest in providing 8,000 undergraduate scholarships to the best foreign students. It also wants existing postgraduate and postdoctoral scholarships to be regrouped and rebranded to increase their visibility.
The reports adds that the national effort should highlight Canada's advantages over the two biggest destinations for overseas students, the UK and the US, such as its lower tuition fees and living costs, and its liberal approach to entrants working during and after degrees.
In particular, it says that Canada should target developing countries where the greatest growth in demand for international higher education is anticipated.
"What is required is a strategy that develops partnerships, including with the private sector, and brings coordination of our various initiatives and a commitment to make strategic investments," the report states. "This will strengthen Canada's engagement with these emerging economies and ensure greater collaboration between institutions [here] and abroad."
The report, presented to Edward Fast, Canada's minister of international trade, on 14 August, was drawn up by a six-strong advisory panel chaired by Amit Chakma, vice-chancellor of the University of Western Ontario.
Other recommendations include improving education visa processing and creating a dedicated Council on International Education and Research.