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.
Nasser al-Bahri - Osama Bin Laden's former bodyguard - has died after a long illness, medical sources in Yemen have told the BBC.