Nash will said he will try to secure a berth in the 2016 Olympic Games in Rio de Janeiro for the Canadian squad, which failed to qualify for this year's Summer Games in London.
The Canadian squad hasn't made an Olympics appearance since 2000, when Nash helped it to a seventh-place finish as a player.
"I'm thrilled to be able to take on this challenge," he said. "We have lots of work to do and I'm excited to get started.
"With the talent we are developing in this country, Canada has an opportunity to become one of the top basketball nations in the world."
Nash is currently a free agent after playing eight seasons with the Phoenix Suns.
The Canadians have been without a coach since the resignation of Leo Rautins in September.