By Diane Bartz and Michael Flaherty

WASHINGTON/NEW YORK (Reuters) - Herbalife Ltd agreed to pay $200 million and change the way it does business to avoid being labeled a pyramid scheme by regulators, a blow to hedge fund manager Bill Ackman who for years has been betting against the dietary supplements maker.

Shares of Herbalife jumped more than 20 percent after the settlement was made public and the Los Angeles-based company said its board had cleared the way for billionaire investor Carl Icahn to boost his stake in the company to as much as 35 percent from his current 18.3 percent.

The stock later pared gains, and was up 9.2 percent at $64.90 in afternoon trading.

Herbalife uses a massive network of independent distributors to sell powdered shakes, vitamins and other tablets designed to help people manage their weight, boost energy and calm stress. The sales method, under which some people get more money for recruiting new distributors than selling products, has attracted criticism.

The company became a battleground for Icahn and Ackman, two of the most outspoken U.S. investors, who became embroiled in a public war of words over their opposing bets. Icahn famously called hedge fund manager Ackman a "liar" and a "crybaby" in a CNBC interview in 2013. They have since made up.

The U.S. Federal Trade Commission opened a probe into Herbalife in 2014 following allegations by Ackman that the company was effectively a fraudulent pyramid scheme.

The FTC said Friday's settlement represented a fundamental change in how the company operates, as it will require rewards to distributors to be based on retail sales rather than recruiting new distributors.

The FTC pointed out that the overwhelming majority of Herbalife's distributors earn little or no money. It remains to be seen how well they will fare under the new arrangement.

Herbalife said that it disagreed with the FTC's criticism but opted to settle with the agency and with the state of Illinois - which had also started an investigation - to avoid litigation.

"The settlements are an acknowledgment that our business model is sound and underscore our confidence in our ability to move forward successfully, otherwise we would not have agreed to the terms," Herbalife Chief Executive Michael Johnson said in an emailed statement.

BATTLE OF THE HEDGE FUNDS

Friday's settlement appeared to be at least a temporary victory for Icahn over Ackman and his Pershing Square Capital Management, which unveiled a $1 billion short bet against Herbalife in 2012.

Pershing, however, argued that Herbalife would collapse under the new operating strictures.

"While it appears that Herbalife negotiated away the words 'pyramid scheme' from the settlement agreement, the FTC’s findings are clear," Pershing Square said in a statement on Friday. "We expect that once Herbalife’s business restructuring is fully implemented, these fundamental structural changes will cause the pyramid to collapse as top distributors and others take their downlines elsewhere or otherwise quit the business."

A day earlier, Ackman said he was still betting against Herbalife shares and that the FTC probe was unlikely to end well for the company.

At the end of June, about a quarter of Herbalife's outstanding shares were held by short-sellers, according to Thomson Reuters data.

Icahn said on Friday it was time for the company to consider strategic opportunities, including potential roll-ups involving competitors, referring to a series of mergers that consolidate a sector.

"While Bill Ackman and I are on friendly terms, we have agreed to disagree (vehemently) on this subject. Simply stated the shorts have been completely wrong on Herbalife," Icahn added in a statement on Friday. (http://bit.ly/29Im6SB)

TOUGH TO IMPLEMENT

Herbalife said it had agreed to restructure its U.S. business so that distributors are rewarded for what they sell, not how many people they recruit.

The company will pay distributors based upon retail sales and provide receipts for their transactions, it said.

"Herbalife is going to have to start operating legitimately, making only truthful claims about how much money its members are likely to make, and it will have to compensate consumers for the losses they have suffered," FTC Chairwoman Edith Ramirez said in a statement. (http://bit.ly/29I0D0a)

The agreement will be difficult to implement, said Robert FitzPatrick, who formed Pyramid Scheme Alert in 2000 to monitor and oppose pyramid schemes.

"Herbalife has agreed and the terms of the agreement are a devastation of the way they operate right now," he said.

Potential difficulties in implementing the changes lie in how the company will differentiate between different classes of buyers: those who buy for personal use, or to distribute; and how to define what constitutes a "legitimate end-user," FitzPatrick said.

Herbalife said that Jon Leibowitz, a former chairman of the FTC, would advise the board of directors regarding compliance with the settlement. Another former FTC commissioner, Pamela Jones Harbour, is already a senior vice president at Herbalife, working on compliance.

(Additional reporting by Sruthi Ramakrishnan in Bengaluru)