Unifor says it filed has an application with the Ontario Labour Relations Board to become the bargaining agent for the more than 6,500 employees at the two plants.
Past attempts at unionizing workers the two plants have been unsuccessful.
Jerry Dias, Unifor national president, declined to say how many of the workers had signed union cards to date, but said Unifor had been sought out by the Toyota employees and had "significant support."
He added: "It's about the Toyota team members saying that they want to have some control over their working lives. It's about them having a real voice.
"Unifor is about strengthening the auto-industry and making sure Toyota workers have a strong voice."
Unifor was created in 2013 by the merger of the Canadian Auto Workers union and the Communications, Energy and Paperworkers union. It currently represents more than 300,000 members in 20 different economic sectors.
Top concerns for Toyota workers include wages, pensions and workplace issues, Dias said, noting that if the certification is successful, Unifor would go into bargaining immediately.
Toyota has three Canadian assembly plants — two in Cambridge and one in Woodstock, Ont. — but Unifor would bargain for all of them as one unit.
On CBC's The Morning Edition Feb. 20, Unifor's director of organizing John Aman said he believed this vote would go through largely because times have changed.
"There's a lot of uncertainty today in the economy, and there's a lot of pressure put on all workers, union and non-union," he said.
"People have told us this [Toyota] is a good place to work, but over the years they've seen a digression of their benefits, their working conditions, and they want to have a voice in their future job security."
Dias said he expected the vote to begin next Monday, and hopes it will wrap up by next Friday. The results will be released later in April.
It is the third attempt to unionize the 6,500 workers at Toyota’s Canadian assembly plants. The International Association of Machinists and Aerospace Workers previously tried to unionize the Toyota plant in 2008, and the IAM and CAW made a joint union drive in 2009.
A recent attempt by the United Auto Workers to get union certification for a Volkswagen plant in Tennessee was rejected.