The move is seen as a sign of Turkish support to Qatar after Saudi Arabia, the UAE, Egypt and Bahrain, among other states, cut diplomatic ties and major transport links with the gas-rich emirate.
The agreement does not contain any specific number of troops to be stationed in the base, or when.
Turkish ambassador to Qatar Ahmet Demirok told AFP last year the base would eventually be home to up to 3,000 troops or possibly more "depending on the needs".
Turkey has close ties with Qatar including in the energy sector, but also maintains good relations with other Gulf countries.
Turkish President Recep Tayyip Erdogan, who was careful not to criticise Riyadh, stood on Tuesday in defence of Qatar and said he intends to "develop" ties with the embattled Gulf state hit by sanctions from Saudi Arabia and its allies.
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