For his work on metals and alloys, he was awarded the Royal Society's Royal Medal in 1869.
In 2009 he was awarded the Royal Medal by the Royal Society "for his outstanding contributions to the understanding of the mechanisms of protein folding and mis-folding, and the implications for disease."
In 1871 he received the Royal Medal of the Royal Society for his chemical researches.
He was awarded the 1968 Petroleum Chemistry Award, the 1988 Linus Pauling Award and has been awarded both the Davy Medal and Royal Medal of the Royal Society, the latter for "elucidating the mechanism of reactions involving free radicals".
In 1889 he won their Royal Medal for his contributions both to cardiac physiology and to the anatomy and physiology of the sympathetic nervous system.
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Möller was educated in Stockholm at Konstfack from 1870 to 1873, and at the Royal Swedish Academy of Arts between 1873 and 1879, when he was awarded with the Royal Medal.
He presented his findings in 1842 in his paper "On the Structure and Use of the Malpighian Bodies of the Kidney" to the Royal Society and was awarded the Royal Medal.