Born in London, Felix Moscheles was the son of the well-known pianist and music teacher Ignaz Moscheles and husband of the painter Margaret Moscheles. His godfather, after whom he was named, was Felix Mendelssohn. His paintings were exhibited in Paris, Antwerp and London.
In 1903 Felix Moscheles became the first president of the London Esperanto club. He was a pacifist and internationalist, and as such also served as president of the International Arbitration and Peace Association. He was involved in attempts to develop international dispute resolution protocols at the Hague.