Helena Foulkes, Hudson's Bay CEO, said, "This agreement is an exciting milestone for HBC as it will deliver important financial and strategic benefits".
The proposed deal reflects a purchase price of $9.45 per unit in cash, representing a total value of $1.74 billion, Reuters reported.
The retailer group's stock jumped more than 44 percent and closed at $6.85 per share following news of the proposal.
The shares traded for $9.16 at mid-afternoon Monday, after hitting a 2019 intraday high of $9.40 earlier in the day.
She admitted publicly in April, during the company's fourth-quarter conference call, that a shift to lower-priced merchandise across the Hudson's Bay chain of department stores had resulted in disappointing revenue.
Hudson's Bay, established in 1670, was taken over in 2008 by Baker's US private equity firm NRDC Equity Partners, which already owned Lord & Taylor.
"If you don't go through these processes, you are really vulnerable to a lawsuit alleging that you shoved this down their throats", said Eric Talley, co-director of the Millstein Center for Global Markets and Corporate Ownership at Columbia Law School in NY.
So far, she's made several bold moves, including the merger that reduced the company's stake in its German operations and the shuttering of its Home Outfitters business in Canada.
The department store retailer also said it pursuing strategic alternatives for the Lord & Taylor business.
In response to analysts who warned of the risks with moving into a culturally different market, Baker said in a June 2015 interview that "people like to throw stones but we think that we're on a very strong course". The stock had lost 13% this year through Friday's close.
Baker's buyout consortium includes Rhone Capital, WeWork Property Advisors, Abu Dhabi Investment Council and Abrams Capital Management. Hudson's Bay said it had set up an independent board committee to evaluate the offer, which is subject to a vote by a majority of shareholders not affiliated with Baker's bid.
'HBC will assume ownership of the Netherlands retail business, and release Signa from its 50.01% back-to-back guarantee of certain obligations of Hudson's Bay Netherlands, ' the company said in a statement on Monday.