Dole Food Co. announced Monday it has accepted a higher offer from its 90-year-old chief executive to go private following two months of talks.

David Murdock has agreed to pay shareholders $13.50 per share in a deal that values the Westlake Village produce company at roughly $1.6 billion, including debt. Murdock, who controls 40 percent of the stock, offered $12 a share in June to buy the company.

The original offer represented an 18-percent premium over the closing price at the time. The new offer represents a premium of about 5.4 percent over the stock’s price at the close of trading Friday, and a 32 percent premium over the closing price at the time of the initial offer.

The deal, which is still subject to approval of a majority of the shareholders not affiliated with Murdock, was unanimously approved by the company’s board of directors. It is expected to close in the fourth quarter. As part of the agreement, the company has a “go-shop” period of 30 days to entertain other offers.

The Los Angeles billionaire, chief executive from 1985 to 2007 before temporarily stepping down, took the company private in 2003 after paying $33.50 a share in a deal valued at $2.5 billion. He then relisted Dole in a $1.1 billion second initial public offering in 2009.

Murdock’s offer follows the $1.7 billion sale in April of Dole’s global packaged goods business and Asia fresh foods business to Itochu Corp., a Japanese firm. The business accounted for about a third of revenue and half of profits.

But the company still remains the largest supplier of bananas, iceberg lettuce and cauliflower to North America. Founded in 1851 in Hawaii, it also supplies produce in 90 countries around the globe.

The deal will be financed through a combination of cash and equity, which shouldn’t be a problem for Murdock. Last year, the billionaire sold the Hawaain island of Lanai for $500 million to Oracle chairman Larry Ellison.

Shares gained 68 cents, or more than 5 percent, to close at $13.49 on the New York Stock Exchange.