JK Rowling also states in Fantastic Beasts & Where to Find Them that a Griffin:

"...originated in Greece and has the front legs and head of a giant eagle, but the body and hind legs of a lion. Like sphinxes (see page 39), griffins are often employed by wizards to guard treasure. Though griffins are fierce, a handful of skilled wizards have been known to befriend one. Griffins feed on raw meat."