FC條頓05

Hammonia shared a common origin with FC St. Georg Hamburg as both sides arose out of the student's group Seminarvereinigung Frisch-Auf; St. Georg was formed first on the left bank of the Alster River, and Hammonia appeared later on the right bank. Hammonia played out its short existence from 1896 to 1904 in the top-flight city league known as the Hamburg/Altonaer Fussball Bund, founded in 1896.

Teutonia joined the NDFV (Norddeutscher Fussball Verband or North German Football Federation) in 1907 and by 1910 had constructed their own ground at Hogenfeldweg. Within another four years the club had captured three local championships. Like many other clubs in the country, it was decimated by World War I and fell to lower league play. They competed in the senior city circuit, the Kreisliga Groß-Hamburg, from 1921 to 1924 and again from 1926 to 1928 before disappearing into lower level play.

Ottensen remained in lower tier ball in the interwar period and through World War II. During the conflict, the team was briefly united with neighbouring association Sportverein Ottensen 07 to play as a combined wartime side known as a Kriegspielgemeinschaft. Disbanded and then later reorganized after the war, the team won promotion to the Verbandsliga Hamburg, Elbestaffel (II) in 1947. The Verbandsliga became the Amateurliga Hamburg where they played until relegated at the end of the 1951–52 season. The previous year the club had captured the Altona Cup, named for the westernmost district of the city of Hamburg.

Teutonia remained a lower-tier club over the next decades until improving somewhat in the early 1990s with a climb into the Landesliga Hamburg-Hansa (V) in 1993. The club was promoted to the Oberliga Hamburg (V) in 2017 and to the expanded Regionalliga Nord (IV) in 2020.

The club participated in the first round of the 2022–23 DFB-Pokal, losing to the RB Leipzig 0–8.