The actor will be voicing the character in director Martin Campbell's adaptation of the DC Comics series.
He told Digital Spy: "Primarily [Tomar-Re] is a completely CGI-created alien, and so I went in and voiced it like an animated film.
"I had voiced an owl in Legends of the Guardian and I'd played a pelican and this guy was half-bird, half-fish with a bit of lizard thrown in. You can't resist."
He joked that shooting CGI films is a "lonely existence" and he had yet to meet co-star Ryan Reynolds, who will play the Emerald Crusader.
The Pirates of the Caribbean star added that he had been a Superman fan before joining the project.
Green Lantern will be released in the US on June 17.
Watch Geoffrey Rush discuss Green Lantern below: