The musician's publicist Sonya Kolowrat said Womack had died yesterday but did not give any other details.
He was diagnosed with Alzheimer's disease two years ago and dealt with a number of health issues, including prostate cancer.
Womack, who appeared at Celtic Connections in Glasgow earlier this year, wrote for some of the biggest names in rock and soul, including the Rolling Stones, Sam Cooke, Janis Joplin, and Wilson Pickett.
He was inducted into the Rock and Roll Hall of Fame in 2009.
Womack was born in 1944 in Cleveland, Ohio, and began singing in a gospel group in the 1950s with his brothers, including Cecil, Curtis, Harry and Friendly Jr.
They recorded two R&B albums as the Valentinos but the group broke up and Womack turned to song writing and a solo career.
He also worked as a session guitarist, appearing on recordings by Aretha Franklin, Ray Charles, Dusty Springfield, and Pickett. From 1970-90, Womack charted 36 singles including That's the Way I Feel About Cha and Woman's Gotta Have It.
A series of personal tragedies including the deaths of two sons led him to drug abuse, according to the Rock n' Roll Hall of Fame.
The star caught the attention of the Stones in the 1960s and influenced many early rockers before fading from popular music for more than a decade.
After a long musical hiatus, in 2009 he was persuaded by Gorillaz co-founder Damon Albarn to record a song for the group's third album. Three years later, Womack released his first album in 10 years, The Bravest Man in the Universe.
Tributes to the US musician flooded in from both sides of the Atlantic.
In a joint statement, released by the Rolling Stones, Mick Jagger, Keith Richards, Charlie Watts and Ronnie Wood said: "Bobby Womack was a huge influence on us.
"He was a true pioneer of soul and R&B, whose voice and song writing touched millions. On stage, his presence was formidable.
"His talents put him up there with the greats. We will remember him, first and foremost, as a friend."
In a personal message, Wood, who inducted Womack into the Rock and Roll Hall of Fame in 2009, tweeted: ''I'm so sad to hear about my friend Bobby Womack - the man who could make you cry when he sang has brought tears to my eyes with his passing.
"My heart goes out to his family & friends and everyone who loved his music. Bobby you will be greatly missed xx."
Singer Rod Stewart spoke of his passion for Womack's 1973 album, Facts Of Life, as he paid tribute to the musician.
In a brief statement, the Maggie May singer said: "I must have listened to Facts Of Life for months. What an influence, what a voice, so long Bobby!"
Gospel singer Candi Staton knew Womack since they were children and she toured with him.
"He had a style that nobody else could ever capture," she said in a statement. "I loved him and I will miss him so, so very much."
Following Womack's death, Blur singer Damon Albarn tweeted: "I will see my brother in church @RealBobbyWomack."
Womack had performed recently at the Bonnaroo Music & Arts Festival in Tennessee and appeared to be in good health and spirits.
He had been scheduled to perform at various events in Europe in July and August, including the Womad music festival at Charlton Park, Wiltshire, next month.
In a statement today, former Genesis singer Peter Gabriel, one of the founders of Womad, said: "I'm very sad to learn of Bobby Womack's death. We were very proud to be having him closing this year's Womad Charlton Park.
"His songs and his voice have been so much a part of the fabric of so many musical lives. In recent years, it was great to see Richard Russell and Damon Albarn bringing his music back into our attention.
"He was a soul legend. Our thoughts and condolences are with his family and friends at this time."