The forward does not want to keep hopping from club to club and hopes he can repay the faith placed in him by coach Walter Mazzarri
The Nerazzurri are his 10th club in as many years - most recently he left Roma for Southampton last summer, where he failed to thrive and spent the second half the season on loan as a back-up striker with Scudetto winners Juventus.
But the 28-year-old, who left the Premier League for a permanent Serie A return this summer, is fed up of constantly swapping clubs and is hoping that he can call San Siro home for many years to come.
“I do want some stability. There's no real reason why I kept changing clubs, but I don’t like looking back," he told La Gazzetta dello Sport.
"I’m happy with my journey so far. They are all experiences. But now I want to stay at Inter for a long time.
"It’s said head coach Walter Mazzarri has wanted to sign me for years and starting at a new club with someone that strongly wanted you was hugely appealing.
"It’s motivating, as I have to prove he wasn’t wrong to put his faith in me. I like his attitude a lot."
Osvaldo has developed a reputation as a bit of maverick in between hopping between clubs but, though he initially hated the "bad boy" tag, he finds it hilarious nowadays and has calmed down somewhat on the pitch.
"Let’s just say that two out of 10 punch up reports are true," he added. "Then there were some fans who hated me and were looking for a scapegoat.
"This ‘bad boy’ label annoyed me at the start, but now I laugh about it. I am a perfectly normal person, but only one thing drives me crazy is injustice. I cannot stand it and, if I see injustice, I lose it.
"I always reacted to injustice and sometimes went too far, putting me in the wrong. I am learning to calm down now.
"It’s true that I tend to leave after a red card or a fight, because I no longer feel respect and that means I don’t feel like staying anymore.
"On the pitch you can say anything you want and I don’t care, but off it you’d best leave me alone. Off the field I am Daniel and anything that happens is my business, so don’t stick your nose in."