"He is already here," Silvio Berlusconi told a news conference in Rome on Wednesday. "He has asked for political asylum and is currently being looked after by the interior ministry."
Earlier in the day, the Italian cabinet unanimously approved the offer of asylum to 41-year-old Abdul Rahman, the prime minister's office said.
"The decision has been made," Roberto Maroni, the welfare minister, said. "The case is resolved."
The move followed an apparent last minute push by members of Afghanistan's parliament demanding that authorities bar the convert from leaving the country.
Shortly before the morning cabinet meeting, Berlusconi said: "I say that we are very glad to be able to welcome someone who has been so courageous."
Giuseppe Pisanu, the interior minister, had earlier said granting asylum would bring with it "all the forms of protection and assistance" related to recognising refugee status.
The jailing of Abdul Rahman in Afghanistan had inspired an appeal by Pope Benedict XVI to Hamid Karzai, the Afghan president, and efforts by the UN to find a country to take him.
Gianfranco Fini, Italy's foreign minister, 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 law.
Abdul Rahman was arrested and brought to trial for converting to Christianity 16 years ago while working as a medical aid worker for an international Christian group helping Afghan refugees in Pakistan.
The pope had interceded on
behalf of Abdul Rahman
Germany, where Abdul 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 Abdul Rahman.
The Roman Catholic church is highly influential in Italian politics, and has been especially vocal in the campaign for next month's election for parliament and the premiership.
However, centre-left opposition politicians have criticised Fini's move describing it as campaign propaganda and saying Italy grants far fewer asylum requests than other major European Union countries.