There is quite the nice article at the English Wikipedia on the topic, also explaining the meaning of the term in German.
I was actually right with my guess that the English usage originates in Nietzsche's "Übermensch":
The crossover of the term "über" from German into English goes back to
the work of German philosopher Friedrich Nietzsche. [...] The term was
brought into English by George Bernard Shaw in the title to his 1903
play Man and Superman. During his rise to power, Adolf Hitler
bastardized Nietzsche's term, using it in his descriptions of an Aryan
master race. It was in this context that American Jewish comic book
creator Jerry Siegel encountered the term and conceived the 1933 story
"The Reign of the Super-Man", in which "Superman" is "an evil
mastermind with advanced mental powers".[...] Throughout the following
decade, Siegel, and Joseph Shuster, recast Superman into the iconic
American hero he subsequently became. It is through this association
with Superman the hero that the term "über" carries much of its
English sense implying irresistibility or invincibility.
So there is a very big difference between the usage of those terms in English and German, they're really "false friends".