Waller studied in Paris, where he obtained the degree of M.D. in 1840, and in the following year he was admitted a licentiate of the Society of Apothecaries in London. He then entered general medical practice at St. Mary Abbott's Terrace, Kensington. He soon acquired a considerable practice, but after the publication of two papers in the "Philosophical Transactions" for 1849 and 1850, he was elected a Fellow of the Royal Society in 1851. He gave up his practice the same year, and left England to live at Bonn and carry on his scientific work. Here he became associated with Professor Julius Ludwig Budge, and published papers in the "Comptes Rendus" for 1851 and 1852, on physiological subjects. For these papers he was awarded the Monthyon prize of the French Academy of Sciences for 1852, and for further work this prize was given to him a second time in 1856. The president and council of the Royal Society also awarded him one of their royal medals in 1860 in recognition of the importance of his physiological methods and researches.