A spokeswoman for Mueller's family -- who learned she was dead in February -
- confirmed the information to CNN.
"We were told Kayla was tortured, that she was the property of al-Baghdadi. We were told that in June by the government," the family told ABC News. The family spokeswoman noted that Friday would have been Mueller's 27th birthday.
Mueller's treatment at the hands of the ISIS leader was first reported by The Independent and ABC News. Details of the reports were confirmed to CNN by multiple sources, including the family representative.
Al-Baghdadi was personally involved in arranging for Mueller to be held in the home of a senior ISIS leader, Abu Sayyaf, after the American was captured in northern Syria in 2013. Sources say the ISIS leader would go to Sayyaf's house where he would sexually abuse Mueller, a humanitarian worker from Prescott, Arizona.
Two Yazidi girls -- members of a small Iraqi minority group that have been among those persecuted by ISIS -- who also were held in Sayyaf's compound gave the U.S. government information about what happened there.
ISIS claims the Quran justifies taking non-Muslim women and girls captive
, that they can be sold as "property," and that rape of captive women is permissible. ISIS spelled out that doctrine in a pamphlet, "Questions and Answers on Female Slaves and their Freedom," distributed after the group seized the Iraqi city of Mosul.
While al-Baghdadi remains the Islamist extremist group's top figure, Abu Sayyaf himself is no longer in the picture, having been killed by U.S. Special Forces
in a raid last May.
The late terrorist's wife, Umm Sayyaf, was captured and was in U.S. custody until this week, when she was handed over to Kurdish authorities in Iraq to stand trial. CNN reported previously that she was was talking to American investigators; ABC News reported Friday that Umm Sayyaf confirmed details of how Mueller was treated.
"We do suspect Umm Sayaaf was a member of ISIL and played an important role in ISIL's terrorist activities," White House spokesman Josh Earnest said last week about her being turned over.
Little is know about al-Baghdadi, who is seldom seen in public. A biography posted on jihadist websites said he earned a doctorate in Islamic studies from a university in Baghdad. Al-Baghdadi was detained for four years in Camp Bucca, which was a U.S.-run prison in southern Iraq.
He was released in 2009 and went on to form ISIS, a brutal militant group that wants to form a caliphate across Syria and Iraq.
Mueller made it her life's work to help others. She graduated from Northern Arizona University in 2009 and worked with humanitarian groups in northern India, Israel, the Palestinian territories and Syria, a family spokeswoman said.
In August 2013, Mueller fell into the hands of hostage-takers in Aleppo, Syria, after leaving a Doctors Without Borders hospital, her family said.
U.S. troops may have come close to rescuing Mueller
in July 2014 when they staged a daring raid at an abandoned oil refinery near Raqqa in Syria in an attempt to find journalist James Foley, who subsequently was executed by ISIS in August 2014, and other hostages.
Troops found evidence the hostages had been there recently, including writings on the cell walls and hair believed to be Mueller's, one U.S. official said.