The deal for the business, which is also behind the Weetos and Ready Brek labels, comes months after Goldman Sachs was hired to handle the sale.
Shanghai-based Bright Food is understood to have struggled in its efforts to make Weetabix palatable to Chinese consumers, who typically prefer hot breakfast dishes.
Post is being advised by Barclays, Rabobank, Credit Suisse and Nomura. The deal is expected to complete in the third quarter.