Hudson's Bay, which operates department store chain Lord & Taylor in the US, said the acquisition would allow it to establish Saks in Canada.
Hudson's Bay, which also runs 90 Canadian department stores, will pay $16 a share for Saks and will also take on some debt.
Both boards have agreed to the deal.
However, Saks shareholders still need to approve the merger.
Saks chairman and chief executive officer Steve Sadove said the transaction offered "compelling value" for shareholders.
"The $16 per share price represents an approximate 30% premium to the 20 May 2013 closing price, the day before media speculation began," he added.
Hudson's Bay, which also operates Canadian homestore chain Home Outfitters, said it would continue to operate Saks as a separate brand, and that it would still be led by key members of its existing management team.
"Saks will remain headquartered in New York City," it added in a statement.
Hudson's Bay said it expected to save $100m Canadian dollars (Â£63.3m) in annual synergies within three years of the merger, which is expected to complete before the end of the year.
US high-end department store chain Saks has been snapped up by Canadian retailer Hudson's Bay Company in a $2.9bn (Â£1.9bn) deal.