The 17-year-old signed a two-and-a-half-year deal at the Stadio Olimpico after several prolific years in Halmstad's youth team.
Berisha also shone for his country, scoring seven goals in as many games as Sweden finished third at the Under-17 World Cup in the United Arab Emirates in November last year.
After wading through the vast number of offers that came his way, Berisha is delighted to have chosen the Italian capital as his destination and is determined to work his way into the first-team picture under Rudi Garcia.
"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."