TRENTON, N.J. — After 34 years as a family-run business, Burlington Coat Factory Warehouse Corp. has agreed to a $2.06 billion cash buyout offer from private equity firm Bain Capital Partners LLC.

Under terms of the deal announced Wednesday, Bain Capital of Boston will pay $45.50 for each Burlington share, a 2 percent premium to its closing price Tuesday. Burlington shares fell 45 cents to close at $44.13 on Wednesday on the New York Stock Exchange.

Headquarters for the 367-store apparel retailer will remain in Burlington in central New Jersey, but the four family members in top management, including 79-year-old founder and Chief Executive Monroe Milstein, will exit the company, said Robert LaPenta, who will stay on as chief accounting officer and treasurer. Chief Operating Officer Mark Nesci will act as CEO until a decision on a replacement is made.

LaPenta said the deal is expected to close within about 90 days.

Bain Capital, one of the world's biggest private investment firms, was the winning bidder of what LaPenta called "a handful" of would-be buyers courting the retailer after it announced in June that it was pursuing options to increase the value of the company.

Burlington said its board of directors has approved the proposed deal, which still requires shareholder approval.

Bain said in a news release it has obtained commitments from members of the Milstein family and related entities representing about 62 percent of Burlington's outstanding shares to vote all their shares in favor of the deal. No date has been set for that shareholder meeting.

LaPenta said the transaction would cause no visible changes to shoppers seeking bargains on coats, clothing, shoes and home furnishings, nor to the retailer's 29,000 employees.

Monroe Milstein said in a statement he was thrilled that the transaction would deliver significant value to stockholders.

Ben Strom, a senior analyst with Variant Research Corp., said he thought the company would have no problem attracting new top managers.

While some of its competitors, such as Ross Stores Inc. and TJX Co.'s T.J. Maxx and Marshalls, have posted better operating margins, Strom said Burlington benefits by paying some of the lowest prices for real estate in the industry. It has also successfully carved out niches in both outerwear and sportswear, and done well in the challenging home-decor business.

A more centralized distribution strategy has reduced clutter on the sales floor, helping to boost same-store sales in recent years, he added.

"They've got a lot of positive momentum they're building on," Strom said.

Strom said the drop in stock price Wednesday could be because the market was expecting a slightly higher per share purchase price. His own company's expectation was $50 per share.

Last month, Bain was part of a group that agreed to buy Dunkin' Donuts and two other restaurant chains for $2.43 billion. Bain is also a one-third owner of Toys R Us, based in Wayne, N.J., which it took private last summer in partnership with Vornado Realty Trust and private equity firm Kohlberg Kravis Roberts & Co.