Interpol has handed over former Trade Minister Abdul Falah Al-Sudani to Iraq's Integrity Commission, Turkey's Anadolu news agency reported.
Al-Sudani, who was arrested in September last year in Beirut, is the first of four ministers convicted of corruption to be extradited.
Al-Sudani was a member of Prime Minister Haider Al-Abadi's Dawa Party, served as education minister during Ibrahim Al-Jaafari's term as prime minister in 2005 and as trade minister in Nouri Al-Maliki's first government from 2006 to 2009.
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Al-Sudani is accused of embezzling state funds through the food rations programme and in 2012 the Iraqi judiciary sentenced Al-Sudani in absentia to seven years imprisonment.
The Iraqi Integrity Commission says four former ministers who fled the country are wanted on charges of corruption including Electricity Minister Ayham Al-Samarrai, Defence Minister Hazem Shaalan, Trade Minister Abdul Falah Al-Sudani and Transport Minister Louay Al-Ors.
Iraqi Prime Minister Haider Abadi, who took office in 2014, pledged to fight the rampant corruption in state departments.