Hasbro, maker of Monopoly and My Little Pony, said that the move to buy the UK-listed firm would "dramatically enhance" its storytelling capabilities.
As well as Peppa Pig, Entertainment One produces other children's cartoons including PJ Masks and new preschool series Ricky Zoom.
"The acquisition of eOne adds beloved story-led global family brands that deliver strong operating returns to Hasbro's portfolio and provides a pipeline of new brand creation driven by family-oriented storytelling, which will now include Hasbro's IP," said Brian Goldner, Hasbro chairman and chief executive.
"In addition, Hasbro will leverage eOne's immersive entertainment capabilities to bring our portfolio of brands that have appeal to gamers, fans and families to all screens globally and realise full franchise economics across our blueprint strategy for shareholders."
Under the terms of the agreement, Entertainment One shareholders will receive £5.60 in cash for each common share.
Peppa Pig, which follows the life of a pink cartoon pig and her family, has been translated into more than 40 languages and is broadcast in more than 180 territories.
A joint statement by Entertainment One and Hasbro said the show had "thrived for over a decade" and "extended itself to new profit streams that continue its success".
PJ Masks also continues to grow, the statement said, with new seasons being launched, new toy lines and a live touring event.
Darren Throop, chief executive of Entertainment One, said there was a "strong cultural fit" between the two companies.
The deal is expected to close in the fourth quarter of the year.
Russ Mould, investment director at AJ Bell, said: "The foreign takeovers keep on coming. Entertainment One has been seen as a bid target for a long time although all the chatter has focused on a media company being the logical suitor.
"The fact that we've got toy company Hasbro attempting to buy the business may initially seem somewhat left-field yet this is a logical tie-up."
Shares in Entertainment One soared 29.5% to 574.5p in early trading on Friday.