Rich was apprenticed to a heraldic designer until 1890, when he entered the Slade School of Art. He was taught by Alphonse Legros and Frederick Brown. He joined the New English Art Club in 1898. He had solo exhibitions at the Alpine Club in 1905 and the Leicester Galleries in 1912. He married Cassandra Berney in 1884. She started a school where Rich was drawing master. On his death the Times obituary called Rich 'the last representative of the great English school of water-colour', comparing his technique to that of John Sell Cotman. He regularly painted directly from nature.