WASHINGTON—Herbalife Ltd. will pay $200 million in a settlement with the Federal Trade Commission that requires significant changes to Herbalife’s business practices but allows the nutritional-products company to avoid being classified as a pyramid scheme.

The settlement, announced Friday, is a dramatic twist in one of Wall Street’s biggest ongoing fights, since avoiding the pyramid label is effectively a victory for Herbalife in its long-running battle with activist investor William Ackman.

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