From 1960 to 1963, he attended the Soviet Naval War Academy in Leningrad and earned a diploma in military science, which he subsequently used to hold various senior positions in the 6th Fleet of the People's Navy.

In 1987, was appointed chief of the People's Navy (who is also Deputy Minister of National Defense) in the rank of vice admiral (two stars).

After his initial selection, Hoffmann was told by the outgoing Defence Minister (Army General Heinz Keßler) that he would be promoted to Generaloberst (colonel-general) in the army; Hoffmann refused to switch services, however, and obtained approval from Egon Krenz (Erich Honecker’s successor) to remain a naval admiral.

After the free 1990 elections, he was succeeded in the ministry by CDU politician Rainer Eppelmann (now called Minister for Disarmament and Defense), but remained commander of the National People's Army until its disbandment and incorporation into the Bundeswehr.

In 1993, Hoffmann published his reminiscences of last days of the National People's Army, Das letzte Kommando; Ein Minister erinnert sich.