According to this websitesite, the change occurred gradually over time, as the representation of the human form in art changed. In the middle ages, artists rarely painted distinctly masculine characteristics on their subjects:
…what modern viewers and artists perceive as “feminine” angels in many famous medieval European paintings were not intended by the artists to be females at all. Particularly during the Medieval period, the overt “sexuality” of much classic Greek and Roman art was almost totally repressed. Bodies were totally covered, both male and female, in long robes.
But artists of the time seldom painted overtly “chiseled,” square-jawed, masculine features on the faces of men. So unless a male was bearded, and particularly if he was represented as a young man, it wasn’t all that easy to sort out the vaguely uni-sex heads in pictures by gender.
In the 1800s, a move toward more realistic depiction of the human form in art coincided with a growing interest in angels apart from their original biblical context:
They may have a “spiritual aura” connected to them, which makes them look otherworldly, but without any special link to a Heaven where God’s throne is. They are viewed by many as being benevolent supernatural beings whose primary interest is helping out people—not necessarily because they have been sent by God to do so, but because it is just “their nature.”
And as this “new” kind of angel has taken shape in the past century or two, the emphasis has shifted more and more to a sort of gentle, nurturing, “motherly” (or “big sisterly”) role for angels—hence the trend toward almost entirely representing them as female.