"He is already in Italy," Berlusconi said. "I think he arrived overnight."
Rahman was released from prison Monday after a court of apostasy against him because of a lack of evidence and suspicions he may be mentally ill.
The Cabinet unanimously approved the asylum Wednesday, the premier's office said.
Earlier, Afghanistan's parliament demanded that authorities not allow the convert to leave the country.
"We sent a letter and called the Interior Ministry and demanded they not allow Abdul Rahman to leave the country," parliamentary speaker Yunus Qanooni told reporters.
Lawmakers spent the day debating the issue but did not take a formal vote on it. Qanooni was, however, speaking on behalf of the entire parliament.
Shortly before Italy's Cabinet meeting, Premier Silvio Berlusconi said Italy would be happy to give asylum to Rahman.
"I say that we are very glad to be able to welcome someone who has been so courageous," Berlusconi told Associated Press Television News.
Interior Minister Giuseppe Pisanu said granting asylum would bring "all the forms of protection and assistance" related to recognizing refugee status.
Pisanu said on Tuesday, anticipating that the Cabinet would approve the request by Foreign Minister Gianfranco Fini for Rahman's asylum, that granting asylum would bring "all the forms of protection and assistance" related to recognizing refugee status.
The jailing of Rahman, 41, in Afghanistan inspired an appeal by Pope Benedict XVI to Afghanistan's president, Hamid Karzai, and efforts by the United Nations to find a country to take him.
Fini had been outspoken about the case from the start, saying Italy had the duty to make plain its "indignation."
Conversion is a crime under Afghanistan's Islamic law. Rahman was arrested last month after police discovered him with a Bible. He was brought to trial last week for converting 16 years ago while working as a medical aid worker for an international Christian group helping Afghan refugees in Pakistan.
Deputy Attorney-General Mohammed Eshak Aloko said prosecutors had issued a letter calling for Rahman's release because "he was mentally unfit to stand trial."
CBS News correspondent Sheila MacVicar quotes one investigator as saying the testimony included a statement from Rahman's daughter, saying that he has mental problems.
Germany, where Rahman once lived, praised the Italian offer.
"This is a humanitarian signal and we welcome it," German government spokesman Thomas Steg said.
Milan daily Corriere della Sera quoted officials of the Italian bishops conference as praising the Italian efforts to help Rahman.
The Roman Catholic church is influential in Italy's politics, and has been especially vocal in the campaign for next month's election for Parliament and the premiership.
Center-left opposition politicians described Fini's move as campaign propaganda and said Italy grants far fewer asylum requests than other major European Union countries.
Italy has close ties with Afghanistan, whose former king, Mohammed Zaher Shah, was allowed to live with his family in exile in Rome for 30 years. The former royals returned to Kabul after the fall of the Taliban regime a few years ago.
Italian troops were sent into Afghanistan after the U.S.-led invasion of the country in 2001 to help with reconstruction.