Its board said it has accepted the sweetened Can$10.30 per share offer on the advice of a special committee's conclusion that the "transaction represents the best path forward for HBC."
The sale must still obtain regulatory and minority shareholder approvals.
Baker has said he hoped to turn around the business, which also owns Saks Fifth Avenue, outside the glare of public markets.
HBC is the continent's oldest company, entwined with the colonization of British North America and Canada's early development.
But amid a changing retail landscape and increased competition from online sales, department stores like HBC have struggled to maintain and attract new customers.
Its top two competitors in Canada, Eatons and Sears, are no more, while new entrants including Nordstrom have popped up recently.
In an effort to streamline and refocus, HBC recently sold off its Lord & Taylor chain and cashed out of European operations.