Apollo will pay $54 per share for CEC Entertainment according to the Financial Times, which cited sources familiar with the matter.
The news comes just a week after Reuters reported CEC was exploring the sale of the business to private equity.
Texas-based CEC, which has a market capitalisation of about $760m, spoke to several interested buyers over the past few months.
Chuck E Cheese was launched in 1977 and now has more than 560 restaurants across 47 US states, most of which are owned and operated by the company.
Deutsche Bank is reportedly leading financing for Apollo’s bid.
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