The Portuguese colonised Brazil in the 16th century. The colonial gardens were based around agricultural plantations (fazendas) and monasteries.
Most of Brazil is tropical (the south is temperate). The tropical climate is very conducive to plant growth so there are many beautiful gardens. But, there are not so many gardens of interest from a design point of view, although the gardens of Roberto Burle Marx are a notable exception. He was a 20th century Brazilian landscape architect and garden designer and his work has influenced garden design worldwide. However, the gardens he designed are found almost exclusively in Brazil. Burle Marx lived at Sitio Roberto Burle Marx, just outside Rio de Janeiro until his death in 1994. The 100-acre site is a national monument and is home to 3,500 plant species. Burle Marx was also an accomplished painter and sculptor and many pieces are on display at the Sitio.
At 340-acres, the Botancial Garden in Rio de Janeiro is one of the largest botancial gardens in the world. It is famous for the row of palms planted when the gardens first opened and a lake full of water lilies (Vitoria Regia). The research institute at the garden focuses on the preservation and research on native flora. Home to the Amazon rainforest, Brazilian flora is extradordinarily diverse and of great global significance. The Amazon rainforest is the most biodiverse tropical forest in the world. On an evolutionary level, South America hes not suffered such climatic extremes as other tropical forest areas so there has been less extinction.
Some companies are starting to offer garden tours in South America. One advantage of booking on to a tour rather than visit as an independent traveller is the tour operators have often arranged access to private gardens that otherwise you might not be able to see or even know about in the first place. Brightwater Holidays offer a 16 night tour Gardens and Natural Wonders of Brazil.