Janssen came from a wealthy, music-loving family and had his first singing lessons in his early youth. He grew up in the family's castle on the Rhine. His family wanted him to study law for the benefit of the family business. They disowned him upon discovering that he had used his law school tuition to study singing instead of law. He did, in fact, study law before deciding to commit to a professional singing career. The night he made his debut at the Berlin Staatsoper, a 12' Bosendorfer concert grand piano was delivered to the opera house with a card saying "welcome back to the family".
In 1922, Janssen was offered his first contract at the Berlin State Opera, starting with small roles but rising in status quickly. A year later, during the 1923-24 Berlin season, he appeared for the first time as Wolfram in Richard Wagner's Tannhäuser. Janssen remained a member of the State Opera's ensemble until 1937. During this time, he appeared as a guest at most of the opera houses and festivals in Europe.
Beginning in 1925, Janssen spent the summer months singing at the Wagner-Festival at the Zoppoter Waldoper. From 1926 until World War II, he regularly sang at the Royal Opera House in Covent Garden, London. Guest appearances led him to the Vienna State Opera, Nationaltheater München, Opera Garnier in Paris, Semperoper in Dresden and the principal operatic theatres in Barcelona and Den Haag. From 1930 to 1937, he sang at the Bayreuth Festival.
He was known to say that he sang opera so he could sing lieder. He made a number of recordings of lieder, in addition to his performances in opera, some of which have been preserved and on CD.
Originally, Janssen sang an extensive repertory. He appeared in Mozart roles such as the Count in Le nozze di Figaro and as Lortzing's Zar Peter in Zar und Zimmermann. He also sang major baritone roles of Giuseppe Verdi, including Conte di Luna in Il trovatore as well as Renato in Un ballo in maschera and Iago in Otello. He also performed Escamillo in Bizet's Carmen.
At the Metropolitan Opera, Janssen was cast overwhelmingly in Wagnerian roles. He was known for his interpretations of Kurwenal in Tristan und Isolde, Amfortas (in Parsifal) and Wolfram in Tannhäuser.
Janssen made commercial gramophone records of some of his roles. There is a recording derived from the 1930 Bayreuth Festival with him performing Wolfram's music, while he sang the role of Don Pisarro in a 1944 radio broadcast of Beethoven's Fidelio with Arturo Toscanini conducting. These recordings have all been re-issued on CD.
Prieberg published the analysis of his private archives under the title Handbook 1933-1945 German musicians in the electronic self-publishing as a resource on a CD-ROM as a pdf file.