He made his operatic debut at Theater Basel as Aufidio in Hans Neuenfels's new production of Mozart's Lucio Silla, and joined the ensemble of Oper Frankfurt in 2018 as its youngest member, where his roles included Tamino, Don Ottavio, Camille in Die lustige Witwe, Alberto in Rossini's La gazzetta, and Flavio in Norma opposite Elza van den Heever. He has since sung the Steuermann in Der fliegende Holländer at the National Theatre in Prague and at the Teatro Regio di Torino, Don Gomez in Weber's rarely heard Die drei Pintos with the Gewandhausorchester Leipzig, and, in the United States, Count Almaviva in Il barbiere di Siviglia with New Orleans Opera and Lyric Opera of Kansas City, and Nemorino in L'elisir d'amore in New Orleans.

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His concert career began early and in Europe: at twenty-four he made his continental debut with the Bayerischer Rundfunk as Christgeist in Mozart's Die Schuldigkeit des ersten Gebots. He has since sung Wagner's Steersman with Jaap van Zweden and the Royal Concertgebouw Orchestra in Amsterdam, Mozart's Requiem with Louis Langrée at New York's Mostly Mozart Festival, Beethoven's Missa solemnis with the NDR Orchestra, Mendelssohn's Lobgesang at the Rheingau Musik Festival, Bruckner's Te Deum and the Mass in B minor in Munich, Bach's Magnificat at Carnegie Hall, and Beethoven's Ninth with the Rochester Philharmonic, the Allentown Symphony, and on tour in Italy and Germany. His performance of Haydn's Die Schöpfung at the Ebracher Musiksommer was recorded for Bayerischer Rundfunk.

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He is a leading interpreter of the Bach Evangelist, having performed all of the Passions, arias, and Evangelist roles, with appearances including the Münchener Bach-Chor, the Milwaukee Symphony, the Hamburger Symphoniker, and Andrea Marcon's Orchester La Cetra in Basel.

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A committed recitalist and interpreter of Lieder and art song, he was awarded the Jean Meikle Prize for Best Duo at the 2019 Wigmore Hall Song Competition with pianist Katelan Trán Terrell. He gave his European recital debut at Oper Frankfurt in songs of Beethoven and Britten, and has appeared at Lincoln Center in Alice Tully Hall and in Britten's Canticles alongside Roger Vignoles and Jakub Józef Orliński.

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Matthew Swensen is a graduate of the Eastman School of Music and The Juilliard School, and was a member of the Wolf Trap Opera Studio and a Gerdine Young Artist at Opera Theatre of Saint Louis.