After finishing his training as a teacher in Küsnacht, he studied Legal science at the University of Zurich.

In 1862, Stössel became the secretary of the Federal Statistics Bureau that was founded two years earlier.

In 1875, he was elected to the Government Council of Zürich, where he served for 42 years,[1] the longest in its history,[citation needed] until 1917.

Stössel was elected to the National Council as part of the Democratic Party.

[1] In 1881, he ran for Chancellor of Switzerland but lost in the fourth round to Gottlieb Ringier.