Boehm (originally "Böhm") was born in Vienna of Hungarian parentage. His father, Josef Daniel Böhm, was a court medal maker and the director of the imperial mint in Vienna. From 1848 to 1851 Boehm studied in London at Leigh's academy of art, the forerunner of the Heatherley School of Fine Art. He then returned to Vienna where he studied model making and medal design at the Academie der Bildenden Kunste before working in Italy and then, from 1859 to 1962 in Paris. In 1856, in Vienna, he was presented with the First Imperial Prize for Sculpture.