Icon made revenues of £18.8m in 2010 and works or has worked with sports organisers including Uefa, Fifa, the Ryder Cup and Wimbledon, as well as sporting event sponsors such as Aviva and Adidas.
Chime sees significant growth opportunities for Icon resulting from the Olympic Games in London in 2012 and Rio in 2016 and in utilising the contacts and relationships with major world sporting federations that Icon will bring to its sports marketing division.
The deal includes an upfront payment of £11m as well as two possible tranches of deferred consideration.
Chime already owns another agency called Icon, which focuses on brand advocacy and is set to win easyJet's advertising account.
Chime did not provide details on the negotiations with the Brazilian sports marketing business beyond highlighting that the next World Cup and Olympics are in the country.
It also stated it was looking at possible healthcare acquisitions.
The company is to raise money for its acquisitions programme by issuing new shares worth £16.1m. A Chime spokeswoman said WPP would keep its existing stake in Chime at 15% by subscribing to new shares.
Chime owns advertising agency VCCP, PR agency Bell Pottinger and sports marketing agencies Fast Track and Essentially.