After completing his primary education, Welti attended the Industrieschule in Zurich, where he studied engraving with Johann Conrad Werdmüller. In 1880, he began a photography apprenticeship with his uncle Oswald Welti in Lausanne, but stayed with him for only one year, enrolling at the Academy of Fine Arts, Munich in 1882. After returning to Zurich in 1886, he became a student and assistant of painter Arnold Böcklin, who would become his main influence. Welti worked at Böcklin's studio until 1891, when he began his career as an independent artist. In 1894, Welti married Emmeline Wildbolz. They settled in the outskirts of Munich the next year, where Welti opened a studio. He worked in Munich until 1908. While there, he became friends with the author Hermann Hesse. Welti’s wife died, suddenly, in 1911. Welti died a year later. His country home in Ostermundigen, near Bern, was bought by Hesse and it was there that Hesse wrote many of his later works. The last years of Welti’s life were dedicated to painting the meeting room of the Council of States at the Federal Palace in Berne, which was commissioned by the Swiss government in 1908. After his death in 1912, the work was completed by Wilhelm Balmer.