US-based Yum!, which already owns 27.2 per cent of Little Sheep, announced in April its plan to take over the firm in a deal that valued it at more than $860 million, and China's commerce ministry gave its go-ahead last November.
In a statement to the Hong Kong stock exchange where it is listed, Little Sheep said on Friday the majority of its shareholders had approved the takeover proposal.
Trading of its shares was suspended on Friday pending the announcement, and will resume Monday. The firm expects the last day of trading on the exchange to be January 12, it added.
Little Sheep is a hugely popular chain of restaurants specialising in mutton-themed hot pot, or so-called Chinese fondue. It has 458 directly owned or franchised restaurants in the country and another 22 overseas.
The commerce ministry's green light surprised some investors, who expected the proposed buy-out to fall foul of China's monopoly laws, which analysts have suggested are used to prevent foreign firms getting a hold in key sectors.
A bid by Coca-Cola to take over China's largest juice maker Huiyuan nearly three years ago, was blocked by authorities who said they were concerned about its impact on competition.
Yum! has nearly 3,500 KFC outlets in China, as well as 560 Pizza Hut restaurants, making it one of the most successful foreign firms in the country. It also owns fast food chain Taco Bell.
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