According to Google Ngram, this phrase has grown in usage since the 1960's.
The problem I'm trying to solve is that American can relate to either an inhabitant of the American continent(s), or an inhabitant of the United States of America. (In fact, the one Brazilian person I know does refer to himself as American, or at least would like to be able to do so.)
I'm looking for a word that specifically means "inhabitant of the United States of America".
I can see that in German, 'US-Amerikaner' is certainly not uncommon (see e.g. Wikipedia). Also, see also the Wikipedia article Names for United States citizens.
Alternatively, if it turns out that "American" always means an inhabitant of the USA, what word can be used for inhabitants of the continent?