Gymboree Corp., the San Francisco-based children’s clothing retailer, has agreed to be bought by Bain Capital for about $1.8 billion, giving the buyout firm a business whose free cash flow has tripled since 2008.

The acquisition price is $65.40 a share, the companies said Monday in a statement. That’s 57 percent more than Gymboree’s closing price on Sept. 30, when reports of a takeover surfaced. Gymboree may seek acquisition proposals from third parties through Nov. 20, according to the statement.

The purchase is the largest leveraged buyout in the retail-apparel sector worldwide over the past three years by more than $1 billion. It gives Boston-based Bain more than 1,000 stores in countries including Canada and Australia. Gymboree, whose sales growth has slowed for three straight years, also operates Janie and Jack shops and Crazy 8 stores in the United States.

“It’s an excellent deal for Gymboree shareholders with a valuation well above what many were expecting,” said Lee Giordano, an analyst at Imperial Capital in New York.

Private-equity firms bought 43 retail-apparel companies over the past three years, with an average deal size of $175 million and an average premium of 15.7 percent, based on the average closing price of the target for 20 days prior to the deal announcement, according to Bloomberg data. Bain is paying a premium of 45.9 percent on that basis.

Gymboree’s annual net income rose to $101.9 million in the year ended Jan. 30, more than triple its profit from 2006.