The incumbent on the account was WPP-owned MediaCom, which attempted to defend the business.
Initiative, part of Interpublic, will be responsible for Hasbro's media planning and buying activities across its entertainment offerings and global brand portfolio.
As part of the business, Initiative will look after children's television channel The Hub, Hasbro's joint venture with Discovery Communications.
Programming from Hasbro for the network is drawn from the toys it markets and includes My Little Pony and The Transformers.
Hasbro produces a range of toys, including board games Monopoly, Pictionary, Taboo and The Game of Life, as well as products such as Play-Doh, Rubik's Cube, Guess Who? and Bop It.
Tim Spengler, president of Initiative North America, said: "Hasbro is a company of iconic brands and an amazing corporate culture."
Hasbro is another in a series of losses for MediaCom in the US.
In December, the shop lost the £900m ($1.4bn) US media planning and buying for GlaxoSmithKline to PHD, and, in October, alcohol giant Diageo moved its estimated $130m media account to Aegis-owned Carat after a review.