Obama also signed an order ending the harsh interrogation of prisoners - including the waterboarding technique that causes detainees to feel like they are drowning.
The prison camp was set up by the Bush administration in 2002 to hold prisoners it detained as part of its so-called war on terror.
Several hundred detainees have since been released but more than 240 prisoners remain there, including Khalid Sheikh Mohammed, who is suspected of planning the September 11, 2001, attacks on the US.
After being transferred to a different area of the prison for those awaiting release from Guantanamo Bay, al-Qurani was allowed to make phone calls and he called Sami al-Hajj, an Al Jazeera cameraman who spent six years in Guantanamo before being released last year.
Al-Hajj said that while the US did have a new administration, "there has been no change in the administration of Guantanamo".
"The people managing the detainees there haven't changed yet. These are the same people who were there during the Bush years and so they use the same methods," al-Hajj said.
Describing a specific incident, which took place after change in the US administration, al-Qurani said he had refused to leave his cell because they were "not granting me my rights", such as being able to walk around, interact with other inmates and have "normal food".
A group of six soldiers wearing protective gear and helmets entered his cell, accompanied by one soldier carrying a camera and one with tear gas, he said.
"They had a thick rubber or plastic baton they beat me with. They emptied out about two canisters of tear gas on me," he told Al Jazeera.
"After I stopped talking, and tears were flowing from my eyes, I could hardly see or breathe.
"They then beat me again to the ground, one of them held my head and beat it against the ground. I started screaming to his senior 'see what he's doing, see what he's doing' [but] his senior started laughing and said 'he's doing his job'.
"He broke one of my front teeth. Of course they didn't film the blood, they filmed my back so it doesn't show."
Al Jazeera provided detailed information of al-Qurani's mistreatment claim to the Pentagon and the US justice department but only received a reply from Navy Lt-Cmdr Brook DeWalt, a Guantanamo spokesman.
"I have no record of authenticity of this," he told Al Jazeera, referring to al-Qurani's accusations.
"It is an alleged phone transcript. ... We don't have any evidence supporting or substantiating any of these claims."
Ahmed Ghappour, a lawyer for Reprieve, a human rights group representing some of the Guantanamo Bay detainees, told Al Jazeera last month that conditions at the facility were deteriorating.
"There has been an increase in the number of reported incidents in Camp Five of Guantanamo Bay, that's one of the isolation camps," he said.
"I filed at least three sets of complaints since December 22 with the military and each one of those complaints called for an investigation, specified guards by number, specified incidents by dates and I've not heard back from a single one of these complaints that I've filed."