A formal announcement is expected later, the Financial Times said.
Weetabix - made in the UK since 1932 - has been widely reported as being up for sale by its Chinese owner Bright Food, which bought a 60% stake in 2012.
Bright's acquisition was the largest by a Chinese firm at the time, but it is believed to have struggled to build significant market share in China.
Chinese consumers generally prefer a hot, rice-based breakfast, rather than cold cereal.
While Weetabix doubled sales in China in 2016, the UK still accounts for the majority of its sales.
Post Holdings is the third-largest cereal firm in the US and owns brands including Great Grains, Golden Crisp and Coca Pebbles.
Some of the world's biggest names in food, including the UK's Associated British Foods and Italy's Barilla, had been named as possible suitors for Weetabix.
Northamptonshire-based Weetabix, which has a royal warrant, was family owned until 2004, when it was bought by private equity firm Lion Capital.
UK cereal company Weetabix is expected to be sold to US firm Post Holdings for $1.8bn (£1.4m), reports say.