Hasbro said the deal would expand its entertainment and “family-oriented storytelling” portfolio.
UK-listed Entertainment One owns other preschool titles including PJ Masks.
The deal is the latest in a string of foreign acquisitions of UK-listed firms including the £4.6bn buyout of pub chain Greene King.
Under the all-cash transaction, Entertainment One shareholders will receive £5.60 for each common share.
“Hasbro will leverage Entertainment One immersive entertainment capabilities to bring our portfolio of brands that have appeal to gamers, fans and families to all screens globally,” the firms said in a statement.
The American toy giant is behind a diverse range of titles including the My Little Pony and Transformers franchises, as well as the Monopoly board game and Play-Doh.
Entertainment One makes a series of film and television titles including the Peppa Pig cartoon.
The firm said the top performing preschool programme has been translated into more than 40 languages and broadcast in over 180 territories.
It is particularly popular in China, where it was first exported in the early 2000s. The cartoon has attracted some 34 billion views on domestic online video platforms.