It will be the first Turkish military facility in the region, Ismet Yilmaz told journalists on the sidelines of three-day Dimdex defence and security fair in Qatar.
"It (the base) will be completed within two years," said Yilmaz, adding the deal had been approved by the Turkish parliament.
The deal is part of a defence agreement concluded by Qatar and Turkey in late 2014, which allows for agreement in the fields of military training and the deployment of the Turkish armed forces on Qatar's territory.
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"We want to achieve cooperation in the field of (military) training and exercises, and contribute to stability in the region," said Yilmaz.
The defence minister said the deal was reciprocal and said there were Qatari military personnel and aircraft currently stationed in Turkey.
Qatar is already home to the biggest air base in the Middle East, Al Udeid, where some 10,000 military personnel are stationed, and is the forward headquarters of United States Central Command.
Qatar and Turkey are increasingly close allies, and both have backed rebels trying to overthrow Syria's President Bashar al-Assad.