He's ten million years old.

From the novelisation by William Kotzwinkle (emphasis mine):

The planet was unspeakably strange. He was ten million years old and had been a great many places, but he'd never encountered anything as complicated as this. Overwhelmed, he crept away, needing to rest his brain in the vegetable patch. He slumped down next to a cabbage and lowered his head. It was all over.

I've also read that he's actually relatively young among members of his species, but can't find a canonical quote for this (I don't actually have the book to hand, although I read it several years ago).