The Italy international feels that his new club may be able to challenge for the Scudetto, which he won last season when on loan at Juventus
The Southampton forward spent the second half of last season on loan at Juventus after falling out with his Saints team-mates and bosses.
He helped ensure that Antonio Conte's retained the Scudetto during his stint in Turin and believes that Walter Mazzarri's side have a chance of doing the same this term.
"I am very happy to be at Inter," he is quoted as saying by La Gazzetta dello Sport.
"Now I have to have my medical before signing, so I don't want to say too much in case of bad luck.
"I hope to do well with my team-mates, and form a partnership with [Rodrigo Palacio and Mauro Icardi] for the sake of Inter.
"The Scudetto? Hopefully."
Osvaldo, who is Southampton's record signing, arrived in England from Roma last August but only managed three goals in 13 Premier League appearances before falling out of favour.