The Romans didn't actually consider the visigoths to be germanic - most of the earlier references to the people we think were goths actually call them 'scythians.' This term was a Roman shorthand for 'barbarians from the east'.

In the 18th and 19th centuries, however, people started comparing different languages to each other, and it was discovered that the language of the Gothic bible (translated by a Roman missionary in the fourth century) was very closely related to the languages spoken in England, Scandinavia, and the countries that now make up modern Germany. This linguistic similarity led some to suggest that the Goths were, in fact, an ancient Germanic people. They then looked at passages like Jordanes' account of the Goths' ancient origins in Scandinavia, and said that the goths mist have been one of the original races of Indo European (or Aryan) peoples, and that they had migrated to the Black Sea before invading Rome. This story, of the Goths as real and original germans, became one of the justifications of Nazi expansion into the Ukraine (ancient Gothic territory!) and, soon after, southern France (which the Visigoths had ruled in the fifth century).

So the connection between Goths and Germanic peoples is a relatively recent one (and often more political than factual), and not really a product of Roman opinions. To the Romans, they were eastern barbarians,mnot northerners.

The reality is harder to pin down. There's no evidence for the mass migration of goths from scandinavia Jordanes tells us about. Almost certainly, the goths came together as a people sometime in the third century.

M. Kulikowsky gives a great introduction to this topic in his book Rome's Gothic Wars.