Born in Leipzig, Backhaus studied at the conservatoire in Leipzig until 1899, later taking private lessons with Eugen d'Albert. He made his first concert tour at the age of sixteen, and continued to tour widely throughout his life. In 1930 he moved to Lugano and became a citizen of Switzerland. He died in Villach in Austria where he was to play in a concert.
Backhaus was particularly well known for his interpretations of Ludwig van Beethoven and Romantic music such as that by Johannes Brahms. He also played chamber music, and made recordings of the Brahms cello sonatas with Pierre Fournier.