Mr Ossoff, 30, the only Democrat in a field of 11 Republicans, was targeted by Mr Trump on Twitter.
Mr Trump derided the result and said that the run-off proved the Democrat could not win.
Mr Ossoff’s campaign slogan was “Flip the 6th” because the election was being run in Georgia’s traditionally Republican Sixth District.
The poll had been called because Mr Trump had named Congressman Tom Price, a Republican, as his Health Secretary.
“This is already a remarkable victory,” Mr Ossoff told the New York Times. “We defied the odds, shattered expectations, and now are ready to fight on and win in June.”
