From 1599 to 1608 he was a pupil of Johannes Eccard, the Kapellmeister of Königsberg. In 1601 he joined the princely Kapelle as a bass singer, and in 1602 he became Kantor at Königsberg Cathedral. In 1626 he succeeded Eccard as Kapellmeister, remaining in the post until his death.
He died at Königsberg.
Stobäus wrote music for liturgical use, as well as songs and compositions for lute. Much of his manuscript music was lost in World World War World War II
What remains is largely held at the Staatsbibliothek zu Berlin. Stobäus"s Commonplace Book, containing songs, instrumental music and drawings of instruments, is preserved at the British Library (Sloane Mississippi 1021).