No, Eternatus is not an Ultra Beast.
Why? Well, I have some reasons.
Why would Game Freak put a UB in Galar? UBs were one of the things that made Alola special, like Hoenn and Secret Bases. I would highly doubt Eternatus is an Ultra Beast from just that knowledge.
The term "Ultra Beast" refers to a creature who comes from the other side of an Ultra Wormhole. Again, that was an Alola thing. I'll post the Shield Pokedex entry in a bit.
If you go to Serebii, Eternatus is listed under "Legendary Pokémon" while Ultra Beasts fall under the "Sub-Legendary Pokémon" category.
Going back to reason #2, here's the Shield Pokedex entry:
It was inside a meteorite that fell 20,000 years ago. There seems to be a connection between this Pokémon and the Dynamax phenomenon.
It came from a meteorite, which doesn't fit in with how Ultra Beasts came to Alola. They traveled through opened wormholes, and not any sort of capsule or meteorite. Eternatus basically just fell from space, there is no evidence that it ever arrived to Galar via Ultra Wormhole.
So no, I'd say that Eternatus is not an Ultra Beast.
Hope this helps! :)