Tetens was the son of a Justizrat (senior counsel) and senator in Danish services.
For many years he captained sailing boats on Hamburg's two lakes, the Binnenalster and the Außenalster, but in the middle of the 1860s he went to Micronesia on behalf of Hamburg shipping owner and merchant Johann Cesar VI.
In 1869 Tetens established the first permanent trading post of J. C. Godeffroy & Sohn.
Tetens later directed the office of the Wasserschout (which managed the central hiring of seamen) of the Hamburgische Admiralität and eventually became a Senator of the "Free and Hanseatic city of Hamburg".
In 1891 he was also joint founder of the German Seaman's Mission in Hamburg.