Yes, this is a word with a long history. As the word suggests, “automagically” is (according to Wikipedia) a blend of the automatic and the magical. Dictionary.com notes that:
“This term is quite old, going back at least to the mid-70s in jargon and probably much earlier. The word `automagic’ occurred in advertising (for a shirt-ironing gadget) as far back as the late 1940s.”
Take charge of your life! Let the Magic do its work! Improve your basic math skills!