Members of the militant group known by its Kurdish initials PKK agreed to leave Turkey following talks between the government and jailed PKK leader Abdullah Ocalan.
PKK commanders last week set Wednesday for the withdrawal to begin.
Pro-Kurdish leaders have expressed frustration that departing guerrillas didn't have security assurances from the government. Opponents of the process said the truce fell short of expectations because the PKK wasn't called on to disarm before leaving Turkey.
The Turkish newspaper quoted the PKK as saying the "first group" of fighters were expected to settle in northern Iraq.
The European Union said it welcomed the measure as part of an eventual accession process. The PKK is listed by the European Union as a terrorist organization.
At least 40,000 people died since the PKK took up arms against the Turkish government in the 1980s.