Cue the Fergie Ferg track, because Alanis Morissette has gone from grunge to glamorous. Isn't it ironic?

TMZ caught the former angry rocker outside NYU's Skirball Center last night -- and girl was looking amazing! Long gone is the scraggly dark hair and bitter temperament that made her famous with "You Oughta Know" back in 1995.

You live, you learn ... how to style yourself!