"There was never any question of detaining or capturing him," the officer told The New Yorker. "It wasn't a split-second decision. No one wanted detainees."
The account conflicts with the Obama administration's claim the raid was "a kill-or-capture mission."
John Brennan, President Barack Obama's counterterrorism chief, said May 2 -- the day of the raid -- the commandos would not have killed bin Laden if they had been confident he was not wearing an "improvised explosive device on his body" or "some type of hidden weapon."
"If we had the opportunity to take him alive, we would have done that," Brennan told reporters at the White House that day.
U.S. officials also said that day it was clear no one at the compound intended to surrender.
The plan was for the Navy SEALs to drop from the helicopters into the compound in Abbottabad, Pakistan, overpower bin Laden's guards, shoot and kill him at close range and then take the corpse back to Afghanistan, The New Yorker said.
When two of the SEALs raiding bin Laden's complex entered his bedroom, one shot one of bin Laden's two wives in the calf and then tackled them both, said the officer, described as "deeply familiar with the bin Laden raid."
The other pointed the infrared laser of his M4 carbine onto bin Laden's chest and fired twice, the officer said.
The first 5.56mm bullet struck bin Laden in the chest, the officer said. As bin Laden, who was unarmed, fell backward, the SEAL fired a second round into his head, just above his left eye.
On his radio, he reported, "For God and country -- Geronimo, Geronimo, Geronimo," The New Yorker said. After a pause, he added, "Geronimo EKIA," for "enemy killed in action."
In the 18 minutes that passed during the assault part of the raid, four men were shot and killed -- bin Laden's courier, the courier's brother, bin Laden's son and bin Laden. An additional 20 minutes were devoted to intelligence gathering, The New Yorker said.
Before dumping bin Laden's corpse into the sea, Brennan, who was earlier a CIA station chief in Saudi Arabia, phoned a former counterpart in Saudi intelligence to find out whether the Saudi government had any interest in taking bin Laden's body.
After all, Brennan said, Bin Laden's relatives were still a prominent Saudi family and bin Laden had once been a Saudi citizen.
"Your plan sounds like a good one," the Saudi replied.