The man, named as Ziyed B, was killed by security forces after attacking a patrol in the airport's south terminal.
Earlier on Saturday he had been involved in a shooting north of Paris and a carjacking in the south.
Prosecutors have opened an anti-terror investigation. Ziyed B had been reported as radicalised in the past, and was on a police watch-list.
He had a long criminal record including convictions for armed robbery, French media report.
The sequence of events
Early on Saturday morning, the suspect was stopped at a checkpoint in Garges-les-Gonesse, north of Paris, where he reportedly lives.
He fired at police with a pellet gun before escaping in a car that was later found abandoned.
He is then believed to have stolen another car at gunpoint from a woman at Vitry, south of Paris. That car was later found at Orly airport.
At the airport the man approached a military patrol. He tried to seize a weapon from a female soldier "in an extremely violent attack", an army spokesman said.
She managed to keep hold of the gun, and two other soldiers opened fire on the attacker, killing him.
The attacker's motivation is not yet known. His home is being searched and his father and brother have been taken into custody - which is standard procedure in suspected terror attacks.
A security operation has taken place at the airport with bomb disposal experts involved and a search for any possible accomplices.
Police say the attacker was not carrying any explosives. No-one else was seriously hurt in either incident.
Travel disruption
Orly - located 13km (8 miles) south of Paris - is the capital's second-largest airport.
Scores of passengers were unable to disembark from aircraft that landed at Orly during the security operation. An estimated 3,000 passengers were evacuated.
"We were sitting in Hall Three when all of a sudden people started running and telling us to run with them," Ellie Guttetter, 18, from the US said.
"The people running were passengers and flight attendants. It was pretty chaotic and everyone was panicking - it was scary."
Another eyewitness, Meredith Dixon, described seeing panicked airline personnel, with no security or police personnel to usher people outside the airport complex.
"It was complete chaos," she told the BBC.
"There were no alarms. No overhead announcements. No organised evacuation. People just began running."
Source : BBC
