In its latest World Economic League Table, the Centre for Economics and Business Research says Asian countries are moving up, while European countries are slipping down the rankings.
CEBR chief executive Douglas McWilliams has told BBC radio that Brazil's advance is part of a wider trend of a shift from west to east and where countries that produce vital commodities are gradually climbing up the economic league table.
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The CEBR also predicted the British economy will overtake France - ranked fifth this year - by 2016 and India, the world's 10th biggest economy in 2011, will move up to fifth place by 2020.
It says the US economy is the biggest, followed by China, Japan and Germany.
