One of rock's most famous voices, who had hits including Proud Mary and The Best, the star died after a long illness.
Turner passed away “peacefully" on Wednesday in her home in Kusnacht near Zurich, Switzerland, according to her publicist.
Beyonce called Turner “my beloved queen” on her website, adding: “I love you endlessly.
“I’m so grateful for your inspiration, and all the ways you have paved the way.
“You are strength and resilience, you are the epitome of power and passion.
“We are all so fortunate to have witnessed your kindness and beautiful spirit that will forever remain.
“Thank you for all you have done.”
Roger Davies, Tina Turner’s manager of 30 years, said: “Tina was a unique and remarkable force of nature with her strength, incredible energy and immense talent.
“From the first day I met her in 1980, she believed in herself completely when few others did at that time.
“It was a privilege and an honour to have been a close friend as well as her manager for more than 30 years.
“I will miss her deeply.”
Among those paying tribute were US President Joe Biden, former president Barack Obama and supermodel Naomi Campbell.
“Before she was the Queen of Rock and Roll, Tina Turner was a farmer’s daughter in Tennessee,” Mr Biden said. “As a child, she sang in the church choir before becoming one of the most successful recording artists of all time.
“In addition to being a once-in-a-generation talent that changed American music forever, Tina’s personal strength was remarkable.
“Overcoming adversity, and even abuse, she built a career for the ages and a life and legacy that were entirely hers.
“Jill and I send our love and prayers to her husband Erwin, the rest of the Turner family, and fans around the world who are mourning today for the woman they agree was ‘simply the best’.”
Mr Obama and former first lady Michelle Obama shared a joint statement to Twitter and Instagram, which described Turner as “raw, powerful and unstoppable”.
“She was unapologetically herself, speaking and singing her truth through joy and pain; triumph and tragedy,” they said.
“Today we join fans around the world in honouring the Queen of Rock and Roll, and a star whose light will never fade.”
In a tribute posted to Instagram, Oprah Winfrey recalled how she had started out “as a fan” of Turner’s and had followed her “from show to show around the country” as a “full-on groupie” before the pair eventually became “real friends”.
“She was a role model not only for me but for the world. She encouraged a part of me I didn’t know existed” she wrote.,
Winfrey added that she was “grateful” for Turner’s courage and that her freedom from her domestic abuse had been “a clarion call for triumph”.
“I’m grateful for her courage, for showing us what victory looks like wearing Manolos and a leather miniskirt,” she said.
“She once shared with me that when her time came to leave this earth, she would not be afraid, but excited and curious. Because she had learned how to LIVE surrounded by her beloved husband, Erwin, and friends.
“I am a better woman, a better human, because her life touched mine. She was indeed simply the best.”
Commenting on Instagram, Campbell said: “Rest in Peace & Power THE QUEEN , LEGEND, ICON. There will never be another. Cherish my times with you.”
Meanwhile, singer Paloma Faith added that she was one of her “greatest influences and inspirations".
“I can't even begin. Really, I can't. Tina you were probably one of my greatest influences and inspirations,” she said.
“I grew up with you in the background of my childhood and all through my time learning my craft I always returned to you.”
American singer Gloria Gaynor hailed Tina Turner as an “iconic legend who paved the way for so many women in rock music, black and white”, while eighties popstar Rick Astley added that she was “one of the greats”.
The Rolling Stones' Sir Mick Jagger, who duetted with Tina Turner during Live Aid in 1985, also told of his sadness at the news of her passing.
“She was truly an enormously talented performer and singer,” he said. “She was inspiring, warm, funny and generous. She helped me so much when I was young and I will never forget her.”
Across her career, which began in the 1950s, the American-born singer won over hearts with classic songs including River Deep - Mountain High, Proud Mary and Nutbush City Limits.
She was a two-time inductee into the Rock and Roll Hall of Fame, and won a total of 12 Grammy Awards.
Turner also turned her hand to the silver screen, and inspired an award-winning musical based on her life before her death.
The Aldwych Theatre, the current home of Tina The Musical on the West End said it was “so proud to tell her story".
The theatre tweeted: “Rest in peace Tina Turner, Queen of Rock 'n' Roll. We are so proud to tell her story on our stage and celebrate such a formidable woman with audiences of all ages.
“Our thoughts are with her family at this time."
A private funeral ceremony will be held for Turner, attended by close friends and family.
She had suffered ill-health in recent years, being diagnosed with intestinal cancer in 2016 and having a kidney transplant in 2017.