OTTAWA—Mark Carney won the leadership of Canada’s Liberal Party on Sunday, putting him in line to replace Prime Minister Justin Trudeau and call an election that suddenly seems winnable for the country’s center left.

Now prime-minister designate, Carney, 59 years old, will officially become Canada’s new leader in the coming days and immediately take over his country’s response to President Trump’s trade war. The former central bank chief of both Canada and the U.K. is expected to quickly call a general election to take advantage of polling momentum against the Conservative Party of Canada, which just weeks ago seemed on the cusp of a landslide.