Weber was awarded the retained business after first triumphing in a competitive pitch for a piece of project work.
Emma Thompson, MD of consumer marketing at Weber Shandwick, said it has been working on "a significant project for the UK market" and has since been appointed as agency of record.
However, its remit does not include the public affairs work awarded to Cohn & Wolfe two years ago, which was the first time it had gone to a UK agency.
The corporate part of Cohn & Wolfe's brief is also understood to have been largely wound down, though Weber will cover some elements.
Scott Wilson, Cohn & Wolfe’s UK CEO and EMEA MD, told PRWeek the agency made a "business decision" in which a change of personnel at the client was a key factor.
Departures from the US-headquarted company include EMEA communications director Helena Roberts, who left last year after a period of maternity leave.
Cohn & Wolfe took the decision despite having added the consumer PR and social media business to its remit during the year.
This followed the resignation of Cake, which had been appointed at the same time Cohn & Wolfe won the corporate and public affairs work in early 2012. It is understood that Cake resigned due to differences of opinion over the direction of its work.
Cohn & Wolfe’s work on the account included handling the reputation management issues arising during the horsemeat scandal in early 2013, when the chain pulled its beef burgers from sale, admitting they could have contained traces of horsemeat from the Silvercrest processing plant.
Wilson said: "We were delighted to be appointed in 2012 to manage Burger King's corporate affairs and public affairs brief and early in 2013 to be invited to take on first the additional consumer brief and then social media brief but we made a business decision before Christmas not to be part of Burger King’s latest comms review.
"We'd thoroughly enjoyed our time working with Burger King and had some fantastic relationships with clients who have all since left the company. Given the changes, we recognised it was the right time to choose not to continue our work with the brand."