Austrian composer best known in the 20th century for having completed Wolfgang Amadeus Mozart's (Mozart, Wolfgang Amadeus) Requiem (K 626).

Süssmayr was educated at Kremsmünster, a monastery school. In 1788 he settled in Vienna and became a music teacher. He became acquainted with Mozart in 1790/91 and sometimes collaborated with him. From 1792 to 1794 Süssmayr was harpsichordist and acting Kapellmeister (musical director) of Vienna's National Theatre; he was Kapellmeister from 1794 until his death. His most notable compositions were Der Spiegel von Arkadien (1794) and music for the ballet Il noce de Benevento (1802).

Süssmayr's handwriting in the manuscript of Mozart's Requiem makes clear that he completed a number of passages after Mozart's death, but the degree to which Süssmayr followed detailed sketches and drafts by Mozart remains a point of dispute.