The first terrorist was killed at the gate by the guards, the second terrorist was killed inside the mess and the third inside the administration building.
In his presser after the attack, Inspector General of Police, Muneer Ahmad Khan, said the airport is "well-guarded and favourable to be used". The three attackers were also killed in a two-day battle.
"Three personnel have been injured. But the state government said no, saying they can deal with it on their own", said a senior government official in the security establishment.
Flights to and from Srinagar International Airport were initially suspended after the attack, but were resumed later on Tuesday.
The terrorists, according to BSF officials are holed up inside the building campus of the 182nd Battalion camp.
The area has a cluster of security installations, including the technical airport used by Armed Forces and VIPs, the Gogo Humhama Air Force Station, and facilities of the BSF and CRPF.
Suicide attackers of the Pakistan-based Jaish-e-Mohammed terror group stormed the BSF camp with guns and explosives on Tuesday, triggering a gunfight that left all three attackers and the trooper dead. The area also houses training centres of the BSF and Central Reserve Police Force.
Kashmiri resistance groups in Jammu-Kashmir have been fighting against Indian rule for independence or for unification with neighboring Pakistan.
One worker who helped the militants reach the camp has been identified, the police said. The base at which the gunbattle took place shares a common compound wall with the airport.
At around 4:10 am today, the three terrorists targeted the BSF camp with indiscriminate automatic gunfire and grenades.
Although the violence appears to be waning, the latest attack has caused alarm across India's security agencies, says BBC Urdu's Riyaz Masroor.
This is the second such attack carried out by the terror outfit recently, after the attack carried one on the district police line in Pulwama.