Saatchi & Saatchi London has held the business since 2014 and was involved in initial discussions with the brand ahead at the start of the review process. The process was handled by ISBA.
Brothers & Sisters and Brokkr, a start-up agency founded by former Abbott Mead Vickers BBDO duo Matthew Turnbull and Daniel Wegrzyn, were also part of the process.
The win for Havas follows the agency's success on picking up the Carling creative business at the beginning of the year.
Like Rekorderlig, Carling is also owned by Molson Coors. Molson Coors bought the UK rights to the Rekorderlig brand in July 2015 from Chilli Marketing.
Commenting on the split, a Saatchi & Saatchi spokeswoman said the agency is "incredibly proud" of its award-winning work for Rekorderlig.
She added: "Sometimes, it's just time to move on. We will always have great affection for Rekorderlig, and wish the brand and Molson Coors every success for the future."
Saatchi & Saatchi created Rekorderlig’s first global campaign featuring two hairy Swedish figure skaters. The spot, called "Silver skaters", ran online and in cinemas.
Clare Wright, head of cider at Molson Coors Brewing Company, said: "Yet again, Havas have proved they are a step ahead of the pack right now. The speed with which their team got to grips with Rekorderlig was incredibly impressive and their strategic and creative rigour will stand us in good stead as we look to grow our share of the cider category."