A sentencing hearing was scheduled for August 9.
Al-Qosi, 50, was charged by the US military of acting as bin Laden's driver and bodyguard and helping the al-Qaeda leader escape to the Tora Bora mountains of Afghanistan after the US-led invasion in 2001.
He was also accused of being part of an al-Qaeda mortar crew.
He entered his guilty plea during a two-hour hearing, during which he said under oath that he provided logistical support for al-Qaeda with the full knowledge that the group engaged in acts of terrorism.
"He admitted he engaged in hostilities against the United States in violation of the laws of war," DellaVedova said.
"Al-Qosi said under oath that he intentionally supported al-Qaeda in hostilities against the United States since at least 1996, when Osama bin Laden issued an order urging followers to commit acts of terrorism against the United States."
Barack Obama, the US president, has pledged to shut down the Guantanamo detention camp but his efforts have been thwarted by the US congress, and 181 prisoners are still being detained.
Most are being held as terrorist suspects, though some have been cleared by the US courts and are awaiting resettlement.