The new offer of $13.50 represents a 32 percent premium to Dole's stock price before Murdock made his initial offer of $12 per share in June.
Dole shares rose 5 percent to $13.45 in heavy midday trading on Monday. They have traded above the $12 level since Murdock, who holds a 40 percent stake in the company, made his first bid.
"We see this raised offer as an attractive transaction that is highly likely to proceed, with a 75 percent chance it goes through at this price level," Janney Capital Markets analyst Jonathan Feeney wrote in a note.
Murdock's attempts to buy the company comes 10 years after he took the seller of bananas, pineapples, berries and packaged salads private for $2.5 billion. The company was listed again in 2009.
Dole has been struggling with volatile demand and low prices for bananas and sold its packaged foods and Asia fresh produce businesses to Itochu for $1.7 billion in April, shrinking its size by a third.
The proposed deal for Dole still requires approval from majority shareholders, but Feeney said Murdock had a strong leverage position as he offered a high premium that other bidders were unlikely to match.
Dole said Murdock would fund the deal with his own cash and equity, and through committed financing by Deutsche Bank, Bank of America and The Bank of Nova Scotia.
The deal, which is expected to close in the fourth quarter, also allows Dole a 30-day "go-shop" period, during which it can solicit offers.
Lazard advised Dole's special committee in the deal, while Murdock was advised by Deutsche Bank Securities Inc.
The deal comes on a day of strong M&A activity in the food and beverage industry.
Packaged foods company Pinnacle Foods said it would buy Unilever Plc's (ULVR.L) Wish-Bone salad dressings business. Campbell Soup Co (CPB.N) said it was in talks to sell some of its European businesses.
