The 17-year-old striker signed a two-and-a-half-year deal at the Stadio Olimpico after impressing in Halmstad's youth team.
"I'm feeling good about [joining Roma]. I've always wanted to play in Italy," he told Solocalcio.se. "Teams wanted me in England and in Germany, and I had a contract from Dortmund in my hands, but I ignored it and signed for Roma the next day.
"Other than Roma and Dortmund, there was also Sunderland, Hammarby, Werder Bremen and Juventus. Sevilla offered me a contract straight after the World Cup and Ajax also got in contact.
"Even so, I wanted Italy. I love the weather and the language, and I've always had an Italian style of play. The plan is to start me off with the Primavera (youth team), let me adapt and then play me in the first team as soon as I'm ready."
Berisha has been compared to his Swedish compatriot Zlatan Ibrahimovic.