Aegis will pay an initial £15.9m in cash with up to £3.4m payable in new shares over five years, subject to performance conditions.
Founded in 1999, AgenciaClick is one of the biggest agencies in the Brazilian market and one of the largest independents in the world with more than 280 staff.
In a trading statement in December, Aegis said that its global digital network Isobar now accounted for an increasing proportion of marketing activity and that the division was making "a significant contribution" to the business.
The latest acquisition will allow Isobar to take advantage of the strong growth prospects in the Brazilian market and use it as a base to expand Isobar in Latin America. Pedro Cabral, AgenciaClick's president, will remain in that position and will also become president of Isobar Latin America.
Robert Lerwill, CEO of Aegis, said: "AgenciaClick has become the market leader for all the right reasons. It is strong across the entire digital spectrum and well known for the outstanding quality of its work. AgenciaClick will give us good exposure to Brazil -- an increasingly important economy of the future -- as well as a world-class brand and team to drive further expansion in Latin America. Altogether, this makes AgenciaClick an ideal addition to Isobar."
The agency, which has offices in Sao Paulo, Rio de Janeiro, Brasilia and Belo Horizonte, has won a string of awards since it was founded eight years ago, including 16 Lions at the Cannes Advertising Festival in the past six years. This includes the first Cyber Lion Grand Prix ever awarded.
Its clients include Coca-Cola, Fiat, Bradesco and Credicard Citi.
The purchase of AgenciaClick takes Isobar into 34 of the world's top 40 markets in terms of broadband penetration.