Kayla Mueller’s family said they were “heartbroken” to learn the news, and released a letter written during her captivity.
Paying tribute to her, President Barack Obama said “she represents what is best about America”.
Last week, Islamic State said Kayla Mueller had died in a Jordanian air strike, without providing proof.
Kayla Mueller was abducted while working in Aleppo, Syria in 2013.
“Our hearts are breaking for our only daughter, but we will continue on in peace, dignity, and love for her,” her family said in a statement.
In a letter written in 2014, Kayla Mueller tries to reassure her family that she is safe and unharmed.
“I could only but write the letter a paragraph at a time, just the thought of you all sends me into a fit of tears,” she wrote.
“I know you would want me to remain strong. That is exactly what I am doing.”
Kayla Mueller’s death was determined after her family was contacted privately by her ISIS captors over the weekend, with US intelligence then confirming the details of the message.
“She has been taken from us, but her legacy endures, inspiring all those who fight, each in their own way, for what is just and what is decent,” President Barack Obama said in a statement.
“No matter how long it takes, the United States will find and bring to justice the terrorists who are responsible for Kayla’s captivity and death.”
Neither the White House nor Kayla Mueller’s family have given the circumstances behind her death.
She was the last known US hostage to be held by ISIS. Three others – journalists James Foley and Steven Sotloff, and aid worker Peter Kassig – were beheaded by the group.
The militants’ claims that Kayla Mueller was killed by a Jordanian air strike were dismissed by Jordan as propaganda.
Kayla Mueller worked with a number of humanitarian organizations at home and abroad. She travelled to the Turkey-Syria border in 2012 to work with refugees.
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