They said Mr Bahri, a Yemeni national, passed away on Saturday in a hospital in the southern city of Mukalla. He is believed to have been in his 40s.
Mr Bahri, also known as Abu Jandal, was also a driver for the late al-Qaeda leader, when he was in Afghanistan.
Mr Bahri was freed from the Guantanamo Bay jail and returned to Yemen in 2008.
He was involved in attacks by Islamist militants in Bosnia, Somalia and Afghanistan during the 1990s, but later renounced al-Qaeda.
In a 2010 interview to the BBC's Newsnight programme Mr Bahri warned that young people in his native Yemen were susceptible to the lure of extremism.
Bin Laden was killed by US special forces in a raid in Abbottabad, Pakistan, in May 2011.

Tara Hudson, 26, from Bath, was jailed at the all-male HMP Bristol for 12 weeks after admitting assault.
Her supporters claim it has placed her in danger of sexual violence and more than 110,000 people have signed a petition calling for her to be moved. Her appeal will be heard on Friday.
Hudson's mother said she was being sexually harassed by other prisoners.
Jackie Brooklyn said her daughter was "constantly" having sexual taunts shouted at her in the jail.
Hudson has had reconstructive surgery and lived as a woman all her adult life but is still legally a man.
The Prison Service said it was a longstanding policy to place offenders according to their legally recognised gender.
"There are strict rules in place to ensure transsexual prisoners are managed safely and in accordance with the law," a spokesperson said on Tuesday.
The appeal against the custodial sentence is scheduled to be heard at Bristol Crown Court on Friday.

7 August 2017 Last updated at 08:13 BST
The two new countries also became independent. This means that they weren't going to be ruled by the British anymore.
This event in history is called the Partition of India.
Many millions of people became refugees as a result of Partition.
Hear one woman's story of how her family were affected.
Watch Finding My Family - Partition: A Newsround special on CBBC at 4:30pm on Tuesday
Nasser al-Bahri - Osama Bin Laden's former bodyguard - has died after a long illness, medical sources in Yemen have told the BBC.
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A transgender woman placed in a men's prison, sparking a wave of criticism, is to appeal against her sentence.
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In 1947, British India split into two new states: Pakistan and India.