In 1818 he published "Observations, systematical and geographical, on the herbarium collected by Professor Christian Smith, in the vicinity of the Congo". In 1822, he was elected a Fellow of the Linnean Society and a foreign member of the Royal Swedish Academy of Sciences. In 1827 he became correspondent of the Royal Institute of the Netherlands, three years later he became associated member. When the institute became the Royal Netherlands Academy of Arts and Sciences in 1851 Brown joined as foreign member. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1849.