I don’t know how long the female version has been around, presumably first in French and now also in English (not to mention Italian Gabriella and German Gabriele).
Although angels are supposed to be genderless, the archangels Michael and Gabriel are treated in English grammar as masculine (taking ‘he’, not ‘she’ or ‘it’ as their anaphoric pronoun), and as personal names are exclusively masculine.
Nevertheless, Michael has now acquired female equivalents — Michelle and the rare Michaela, and Gabriel has likewise acquired Gabrielle. As for other archangelic names, I’ve never come across a female form of Raphael or Uriel.
Interestingly, in standard spoken French the masculine form Gabriel and the feminine form Gabrielle are homophonous, both ɡabʁiɛl; though the feminine form has a final phantom ə that can surface in singing or in regional (southern) speech.
But in English the female form is regularly stressed on the final syllable, which gets a strong vowel, and is thus distinct (usually!) from the male form, which has initial stress and a reduced vowel in the last syllable.
Compare Daniel, the prophet cast into the lions’ den. As a man’s name in English he is ˈdæniəl, and again there is now a female form ˌdæniˈel, spelt in English as Danielle, though the French form is actually Danièle (again homophonous in French with the male form, give or take a schwa).
I don’t know enough about French to know why Gabriel forms the feminine by doubling the l while Daniel does it by adding a grave accent (but compare appeler — j’appelle as against geler — je gèle). Nor do I know enough about the history of English to know why Gabriel ends up with eɪ but Daniel with æ from what was presumably the same vowel in Latin/Greek/Hebrew (for the quantity of a in these phonetic contexts, compare Abraham and germanium).