There aren't any hard genetic borders in Europe; all peoples look pretty much like their neighbours, but if you go far enough the accumulated differences add up to the rather marked difference in looks 'tween, say, Swedes and Sicilians.
The Goths aren't recorded as having lived in Germany BTW. They first turn up in modern Poland, then immigrate to the Ukraine, and then the Balkans before ending up in Italy. (Not all researchers accept the identification of the early Goths at the Baltic with those turning up generations later in the Ukraine.)
Edit: The big point, tho, is that modern genetic surveys have concluded that the Germanic contribution is very small. Since even the declined Roman population of Italy in the dark ages counted in the millions, and the Germanic invaders probably in the tens of thousands, that should not be surprising.