The singer, whose career has spanned seven decades, died at her home in Detroit, Michigan, at 9.50am on Thursday, her publicist said.
A statement from Franklin's family, via the singer's long-time publicist Gwendolyn Quinn, said that she died "surrounded by family and loved ones".
The statement continued: "Franklin's official cause of death was due to advance pancreatic cancer of the neuroendocrine type.
"In one of the darkest moments of our lives, we are not able to find the appropriate words to express the pain in our heart. We have lost the matriarch and rock of our family. The love she had for her children, grandchildren, nieces, nephews, and cousins knew no bounds.
US gospel artist Jocelyn Brown joined in with tributes being made around the world and told Premier she was hoping that Franklin wouldn't die yet.
Speaking to Lady D on Premier Gospel, she said: "I wanted more from her but God has his own way."
She added that she was comforted knowing that the star "knew prayer" and was "with the Lord".
The family's statement thanked people for their support since news broke that the singer was seriously ill.
"We have been deeply touched by the incredible outpouring of love and support we have received from close friends, supporters and fans all around the world," the family said.
"Thank you for your compassion and prayers.
"We have felt your love for Aretha and it brings us comfort to know that her legacy will live on. As we grieve, we ask that you respect our privacy during this difficult time."
Quinn added that "funeral arrangements will be announced in the coming days".
The music icon, known for her hits such as Respect, Think and (You Make Me Feel Like) A Natural Woman, died several days after she was reported to be seriously ill.
In recent days, the ailing star had been visited by Stevie Wonder, the Rev Jesse Jackson and her ex-husband, actor Glynn Turman.
Former US president Bill Clinton and his wife Hillary paid tribute to "one of America's greatest national treasures".
They said in a statement: "For more than 50 years, she stirred our souls. She was elegant, graceful, and utterly uncompromising in her artistry.
"Aretha's first music school was the church and her performances were powered by what she learned there. I'll always be grateful for her kindness and support, including her performances at both my inaugural celebrations, and for the chance to be there for what sadly turned out to be her final performance last November at a benefit supporting the fight against HIV/Aids.
"She will forever be the Queen of Soul and so much more to all who knew her personally and through her music. Our hearts go out to her family and her countless fans."
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