The move follows Adidas' acquisition of rival company sports firm Reebok, which recently signed Thierry Henry from Nike.
Aegis-owned Carat fought off OMD in a final head-to-head pitch after Starcom and MediaCom had earlier withdrawn from the process.
The decision means that the UK Adidas and Reebok accounts move from PHD and OMD into Carat.
Prior to the pitch, Carat handled the Adidas business globally with the exception of the UK. OMD handled Reebok across Europe.
Uli Becker, Adidas's head of global brand marketing, said: "We were fortunate to have two very qualified agency finalists, OMD and Carat, who continued to raise the bar every time we met with them. This was a tremendously difficult decision for all the key stakeholders from the group because of the high calibre of the agencies' teams.
"We chose Carat for their strong strategic vision and their commitment to our business. We are confident that Carat will extend our successful partnership to deliver growth of the adidas and Reebok brands through the World Cup to the Beijing Olympics and beyond."
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