Italy's Prime Minister Silvio Berlusconi told a news conference in Rome that Abdul Rahman "is already in Italy, he has requested political asylum and is currently under the care of the interior ministry."
The 41-year-old's case casued an international outcry and was seen as a key test for Afghanistan's fledgling democracy. But Afghan parliamentarians have denounced Western "interference" in the case.
"The decision has been taken. The matter has been resolved," Labour Minister Roberto Maroni said in Rome, announcing the asylum offer.
Mr Rahman was arrested about two weeks ago under Islamic Sharia law that dictates that he should be sentenced to death unless he reverts to Islam. The Afghan constitution is partly based on the Islamic code.
Mr Rahman was freed from jail in secret late on Monday and kept under tight security at an undisclosed location after calls for him to be put to death.
His release came after Afghanistan’s Supreme Court suspended its case against him saying it had doubts about Mr Rahman's mental health after testimony from his relatives that he was "mad".
Kabul's Western allies, on whom it depends to rebuild after years of war, put unprecedented pressure on Afghanistan’s new democratic government to honor freedom of religion.
Afghan President Hamid Karzai held several meetings at the weekend to try to find a way to resolve the issue the "serious crisis" for the government.
Interference denounced
But Afghanistan's parliament denounced the "interference" in a heated debate on Wednesday and said Mr Rahman should not be allowed to "escape".
The Supreme Court's weekend decision to release Rahman from trial was "contrary to the laws in place in Afghanistan," said a summary of the debate read out by speaker Yunus Qanooni and approved by MPs.
Mr Rahman converted in Pakistan about 16 years ago and lived in Europe, including Germany, for some time before returning to Afghanistan around three years ago.
The premier of Germany's Saarland state, Peter Mueller, had also offered him asylum, telling the German daily Die Welt he would be "warmly welcome".
The case is being seen as a test of how far the conservative country has moved on from the 1996-2001 rule of the hardline Islamist Taliban, who were removed in a US-led operation after the September 11, 2001 attacks.
The Taliban strictly implemented Sharia punishments including chopping the hands off thieves.