Mario Balotelli's agent Mino Raiola has revealed that the striker will not be leaving Anfield this summer.
Graham Dorrans has signed a two-year deal with Norwich City following a successful loan spell with the club.
The Italy international moved to the Barclays Premier League club last month in a club-record deal worth a reported £15million and is delighted with his decision.
"I was really looking forward to having an experience abroad and I believe I have made the right choice," Osvaldo told the Gazzetta dello Sport.
"I am happy in England and I feel good with my new team-mates and club.
"I still have to adapt and score goals but I am more than happy with my decision."
Osvaldo, who signed a four-year contract with the Saints, admitted he had been struggling with life at Roma in recent months.
The 27-year-old was at the receiving end of criticism from a section of Giallorossi fans who were left frustrated by the club's disappointing season.
Roma finished sixth in Serie A and failed to qualify for Europe and, to rub salt into the wounds, the capital club then surrendered the last available Europa League qualifying spot to arch-rivals Lazio by losing the Coppa Italia final.
"I don't feel as though I'm in exile," Osvaldo said. "This was my decision even though Roma wanted me to go.
"I could no longer be at Roma and receive threats and insults.
"It's not normal to have abusive messages written on the walls outside your house, especially because I don't deserve them.
"The majority of the Roma fans were supportive and showed me affection but there were others that don't show support in the right way and fortunately, they are a minority.
"I just needed calm and tranquility and that is why I have chosen England. I have no regrets."
Osvaldo, who is currently on international duty with Italy ahead of Tuesday's World Cup qualifying meeting with the Czech Republic, joined Roma from Espanyol in 2011 and scored 16 goals in Serie A last season.