Godin, 21, has signed a five-year contract with Villarreal, while Rossi spoke to the media yesterday: "I hope to be able to score many goals to help the team.
"I have seen a lot of Spanish football on television when I was in England and I liked it.
"As well as that, Villarreal are a great team and they have shown it in the effort they have made to sign me."
Of his new team-mates, Rossi already knows plenty about former France winger Robert Pires.
"He is a great player. I have already seen him play at Arsenal. He has a lot of titles and experience," Rossi added.
Villarreal president Fernando Roig said of their new addition: "He is a young player who we have followed for a long time, and in whom we place a lot of confidence. He scores goals, which is what we need."