The prosecution agency did not provide any explanation for Italy's move, saying simply that the Italian justice ministry had informed its Norwegian counterpart in a letter that the request would be "withdrawn."
A refugee in Norway since 1991 but not a citizen, 60-year-old Krekar -- whose real name is Najumuddin Ahmad Faraj -- is suspected by Italian police of leading the Rawti Shax, a network with alleged links to the Islamic State group and which is suspected of planning attacks in the West.
Norwegian officials had perceived the extradition request as a blessing for their country, which has been struggling for more than 10 years to rid itself of a man seen as troublesome.
Considered a threat to national security and featuring on UN and US terror lists, Krekar has been at risk of deportation since 2003.
While courts have upheld the ruling, Norwegian law bars him from being deported to Iraq, because he risks the death penalty there.
Having spent several years in a Norwegian prison for threats and inciting violent behaviour, he was again imprisoned on November 23 after exhausting all the legal options to prevent his extradition to Italy.
Krekar's lawyer, Brynjar Meling, hailed the withdrawal of the extradition request as "a victory of the law".
"This shows that it is not possible to conceal an expulsion behind a request for extradition. This decision is a defeat for those who tried," he told Norwegian media.
Krekar was released from custody on Wednesday.
"I had no idea I was getting out. I had received no information," he told daily VG, saying it was "great" to be free.