The Syrian Observatory for Human Rights said there were still clashes taking place on the outskirts of the airport, but that it was under control of the militants.
Observatory director Rami Abdel Rahman said the bodies of "dozens" of Syrian troops killed in the battle for the airport were still inside the facility.
Syrian state television, meanwhile, said troops had staged an "evacuation" of the airport after heavy fighting.
"After heavy fighting by the forces defending the Tabqa airport, our forces implemented a regrouping operation after the evacuation of the airport," state television said in a breaking news alert.
It added that troops were launching "precision strikes" against "terrorist groups" in the area, inflicting heavy losses.
The capture came after IS fighters launched a fourth assault on Tabqa overnight, in a bid to cement their control over Raqa province.
Earlier, Abdul Rahman said the militants had begun advancing into the airport, hanging up the head of a decapitated soldier at one of the checkpoints they had seized.
Islamic State fighters have been trying to take Tabqa since early August, but began assaulting the airport in earnest on Tuesday.
At least 100 Islamic State fighters and 25 regime troops had been killed before the latest clashes.
The airport was the last army stronghold in Raqa, after militants captured Brigade 93 and Division 17 in the northern province, killing dozens of soldiers, many of whom were beheaded.
Raqa has become the stronghold of the Islamic State, which controls the provincial capital and has declared an Islamic "caliphate" in territory it holds in Syria and Iraq.
The group initially fought alongside Syrian opposition groups, but its abuses sparked a backlash from rebels who pushed it out of parts of northern Syria.
In recent weeks, though, IS has advanced back into areas it withdrew from, including in northern Aleppo province.
Elsewhere, however, the Observatory said IS fighters were pulling out of parts of central Homs province.
The monitoring group said there was no official reason given for the withdrawal, but that the militants appeared to be moving to areas under tighter IS control, including Deir Ezzor province in the east.
The Observatory said several areas in Homs that had been under IS control were taken over in the wake of the withdrawal by rival jihadist group al Nusra Front, which is al Qaeda's Syrian affiliate.
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