"This morning at 9:40, our Rafale planes carried out a first strike against a logistics depot of the terrorist organisation Daesh in north-east Iraq. The objective was hit and completely destroyed," Hollande's office said in a statement, using an alternative name for the Islamic State extremist group.
"Other operations will follow in the coming days," added the statement from Hollande's Elysee Palace office.
"The prime minister will inform parliament next week about the conditions of our forces' engagement at the side of the Iraqi armed forces and the Peshmerga (Kurdish fighters) to weaken Daesh and restore Iraqi sovereignty," the statement added.
"I decided to respond to the request of the Iraqi authorities to offer aerial support," Hollande told reporters.
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"As soon as we have identified targets, we will act... within a short time-frame."
France has already conducted reconnaissance flights over Iraq that started Monday and dispatched weapons to the Kurdish forces fighting the IS group.
Hollande himself visited Iraq late last week - the most high-profile leader to do so since jihadists stormed across the country - and Paris hosted an international conference on the crisis Monday.
"We will not go further than that. There will be no ground troops and we will only intervene in Iraq," said the president.
France has six Rafale fighter jets and just under 1,000 soldiers based in the United Arab Emirates and could even mobilise an aircraft carrier, the Charles de Gaulle.