The frontman joined the Giallorossi over the weekend after the capital club bought the remaining 50 per cent of the player from Serie A rivals Parma.
He had spent last season on loan at the Stadio Olimpico, scoring nine goals in 24 league appearances.
Speculation had linked the 21-year-old with Liverpool and a reunion with former boss Brendan Rodgers, who he worked under while on loan at Swansea from Chelsea.
But Borini, currently part of the Italian squad at Euro 2012, says he was only ever focused on staying at Roma and was not distracted by talk of an Anfield move.
He told The Sun: "I am a Roma player.
"It's not my business that there is talk about whether I go to Liverpool or stay. It doesn't matter to me, I am at Roma."
Even his agent agreed that Borini never had any intention of leaving Roma this summer.
"Since the first day he moved to Roma, Fabio's wish has been to become a Roma player," Borini's agent Marco De Marchi told Italian radio Tele Radio Stereo.
"We had hoped that the clubs would find an agreement and we had to wait.
"Now we can say that we are very happy.
"Fabio is delighted and is ready to begin a true new adventure with Roma.
"We want to thank Parma, the club that brought Borini back to Italy, Roma and especially (Roma sporting director Walter) Sabatini, who has done an extraordinary job."
De Marchi is not surprised several clubs have expressed an interest in 21-year-old Borini, who is currently on international duty with Italy at the European Championship.
"When a young player does well in his first year in Serie A, it's normal that they are monitored by top international clubs," he said.
"(Parma president Tommaso) Ghirardi had declared many times that several important clubs had shown an interest in Borini but that was it.
"The player's wish was clear from the first day and hence, nothing came of those interests and the situation was resolved for the best."