The Aegis agency took the business in a final shoot out against WPP's MEC and Ominicom Group's Manning Gottlieb OMD.
Stuart Newman, managing partner at Vizeum, said: "This is an awesome win and it's great to work with the market leader in a highly competitive sector."
The account was previously held by independent agency the7stars, who declined to pitch for the account when the review was called last month.
Procurement consultant Tina Fegent is understood to have assisted William Hill in running the pitch process.
William Hill's creative agency, Beattie McGuinness Bungay became the third to work with the bookmaker within a year when it was appointed in January and is unaffected by the media review.
Earlier this year, William Hill signed up to sponsor the UK coverage of the Italian, Russian and Dutch football premier leagues on the sports broadcaster ESPN.
BMB had followed Brooklyn Brothers and The Bank on the William Hill business and has created a series of ads focusing on William Hill's betting services. Spots feature flashing words and images to communicate its range of services and technology.
The win closes a resurgent year for the Aegis network, with sister agency Carat picking up the £28m media business for price comparison site Gocompare.com and the £23m account for builders merchants Wickes.
In June, car marque BMW appointed Vizeum to its consolidated £23m media planning and buying account.
The agency, which was the incumbent on the main buying business, also added the digital planning and buying account that was previously handled by ZenithOptimedia Group.
Follow Mark Banham on Twitter @Banham72