Nadir was convicted in 2012 of the theft of nearly £29m from the major UK conglomerate in the late 1980s.
He was jailed for 10 years after an Old Bailey trial, and ordered to pay £5m in compensation.
The Ministry of Justice (MoJ) said he had now paid £2m in legal aid and the compensation, and could be transferred.
An MoJ spokesman said: "It is right that foreign criminals are properly punished but not at the expense of British taxpayers.
"This government is committed to removing foreign criminals to their own countries. Since Asil Nadir has now repaid the £2m he owed the Legal Aid Agency, plus £5m in compensation he paid earlier,  arrangements were made with the Turkish government for his removal as part of our Prisoner Transfer Agreement."
After Polly Peck collapsed amid a Serious Fraud Office investigation, Nadir fled the UK in 1993 while awaiting trial and went to northern Cyprus. He returned to the UK in ill health in 2010.
Polly Peck International began as a small fashion company but expanded into the food, leisure and electronics industries under Nadir's ownership, growing into a business empire with more than 200 subsidiaries worldwide.
Tycoon Asil Nadir, who was jailed in the UK for stealing millions of pounds from his Polly Peck empire, has been transferred to a prison in Turkey.