Burger King kicked off the review, which also included Mexico, in early December in a bid to achieve greater consistency and cost efficiencies.
Carat had handled the UK part of the business since 2000. It also handled it in Germany.
The fast-food giant spends £10 million per year in the UK, according to Nielsen Media Research.
Burger King originally drew up a longlist of agencies, which was shortened to Initiative, Carat and MindShare at the beginning of the year.
The pitch was carried out on a market-by-market basis, with each territory ranking the three agencies in order of preference.
Media sources said the appointment of a new media agency has been delayed by a reshuffle in the Burger King marketing department.
Burger King declined to comment.