Born at Rostock, Germany, died Melbourne, Australia.
He studied pharmacy and took his Doctor of Philosophy at the University of Kiel in 1847. He came to Australia in 1848 for health reasons and became a great botanical collector and writer. He was Victorian Government Botanist from 1853, and for a time Director of the Botanic Gardens. He travelled widely in Victoria and was on the A.C.Gregory expedition to northern Australia in 1855-57. He supported botanical exploration and collecting throughout the colonies.
His botanical publications are very extensive, and include Fragmenta Phytographiae Australiae published over the period 1858-82.
Dr Mueller received honours from many of the ruling Royal Houses of Europe, he was made a Baron by the King of Wurtemberg in 1871, and knighted by Queen Victoria.