One had been held for 10 years after being captured by British forces in Iraq and transferred to Afghanistan, said legal charity Reprieve.
US authorities say that the detentions are necessary to keep potentially dangerous men off the battlefield.
It was not immediately clear where the 10 released men had been taken.
Justice Project Pakistan, which is providing representation to some of the detainees, said the International Committee of the Red Cross had informed their families that the prisoners had been released, but not where they were.
Another batch of six prisoners was released in December, only to be secretly transferred to Pakistani prisons and held incommunicado for several weeks.
Pakistani authorities did not tell the families the US had freed the six and only acknowledged holding them after Justice Project Pakistan won a series of court orders.
Foreign prisoners at Bagram, sometimes dubbed "Afghanistan's Guantanamo Bay", face review boards staffed by US military officers but are not allowed to know all evidence against them or be represented by a lawyer of their choice.
The boards evaluate the evidence and whether the detainees might pose a future threat to US forces.
Sarah Belal, a lawyer at Justice Project Pakistan, said dozens of men remain in the prison under US custody.
She said Pakistani government officials needed to tell lawyers and families about releases.
Pakistani authorities did not return calls seeking comment.
COMMENTS (1)
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The news is faulty; the Americans no longer control the Bagram Prison, but the Afghans do. Pakistanis should thank Hamid Karzai for this jesture.
Rex Minor