There is quite the nice article at the English Wikipedia on the topic, also explaining the meaning of the term in German.

I actually was quite 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".

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".