Bessel was elected a member of the Prussian Academy of Sciences in 1812 and of the French Academy of Sciences in 1816, a foreign member of the Royal Swedish Academy of Sciences in 1823, and a fellow of the Royal Society in 1825. In 1832, he was elected a Foreign Honorary Member of the American Academy of Arts and Sciences. In 1827 Bessel became member of the Royal Institute of the Netherlands, predecessor of the Royal Netherlands Academy of Arts and Sciences.