Born in Lyon, France, he studied trumpet with Francois Dauverné at the Paris Conservatoire from 1841 to 1845. He was appointed professor of saxhorn at the École Militaire in 1857, and became professor of cornet at the Paris Conservatoire in 1869, where Merri Franquin was among his students. He published his Grande méthode complète pour cornet à pistons et de saxhorn in Paris in 1864. This method, which is often referred to as the "Trumpeter's Bible," is still studied by modern brass players. His variations on The Carnival of Venice remains one of the great showpieces for cornet soloists today.
Arban apparently made a phonograph cylinder recording for the Edison Company shortly before his death. Arban died in Paris on April 9, 1889.