Ochman began learning voice under the direction of Gustaw Serafin in Kraków (1955–1959) and Maria Szłapak in Bytom (1960–1963). In 1960, he joined the Silesian Opera in Bytom, where he sang for three seasons, in 1963 and 1964; and then, at the Opera Krakowska. He performed at the Teatr Wielki in Warsaw from 1964 till 1970. In 1965 he sang the tenor lead Jontek in the "national Polish opera" Halka by Stanisław Moniuszko in the opening performance in the reconstructed Teatr Wielki. He recorded that role and it is now available on compact disc.
Wiesław Ochman began his international career in 1967 with the Opera in Berlin. He sang in Munich and Hamburg. He achieved his first successes in competition at festivals in Glyndebourne and Salzburg. In 1972, he was engaged by the Paris Opera, and consecutively by operas in Chicago and San Francisco. In 1975 with the role of Arrigo in the opera The Sicilian Vespers by Giuseppe Verdi, Ochman made his debut at New York's Metropolitan Opera.