Born in Vienna, Wächter studied at the University of Vienna and the Vienna Academy of Music. In 1953, he began voice lessons with Elisabeth Radó. That same year he made his operatic debut, as Silvio in Ruggiero Leoncavallo's Pagliacci, at the Vienna Volksoper. In 1954, he debuted at the Vienna State Opera. In 1956, he debuted at Covent Garden, as Count Almaviva in Mozart's The Marriage of Figaro, and at the Salzburg Festival, as Arbace in Mozart's Idomeneo; in 1958, at Bayreuth, as Amfortas in Wagner's Parsifal; in 1959, at the Paris Opera, as Wolfram in Wagner's Tannhäuser; in 1960, at both La Scala and the Lyric Opera of Chicago, as Count Almaviva; and, in January 1961, at the Metropolitan Opera, as Wolfram. In 1963 he was awarded the title Kammersänger. In 1980 he created the role of Joseph in Gottfried von Einem's Jesu Hochzeit, opposite Karan Armstrong. In 1969, Wächter appeared as Don Giovanni on the set of postal stamps issued by Austria to commemorate the centenary of the Vienna Staatsoper. In 1987 he became general manager of the Vienna Volksoper. In 1991 he also became head of the Vienna State Opera, a position he held at the time of his death. Wächter died in 1992 of a heart attack while walking in the woods of Vienna.