The appointment ends a 20-month relationship between Admiral and incumbent WPP agency Mindshare, which decided not to repitch for the business.
The pitch process was handled by the AAR and led by Admiral's media strategy manager, Emma Dunn.
Marc Mendoza, chief executive of MPG, said he was "delighted" with the win, adding: "It's fantastic to be working with a collection of prestigious insurance brands and I know we can work together to significantly grow these brands.''
The review of the group's media requirements comes as the insurance industry faces increasing competition online.
Established in 1993, Admiral is the trading name of financial and insurance company EUI.
For the past eight years, the group's work has focused on providing online car quotes for drivers, including higher risk categories such as young drivers and high-performance cars.
Elsewhere, the £25m media business for Admiral's Confused.com, held by McCutcheon Norveil Consultancy since 2002, was awarded to Omnicom's PHD at the end of March.