"Body and Soul" will go on sale next month with proceeds going to the newly established Amy Winehouse Foundation, the singer's family said.
The two singers recorded the song in March at London's Abbey Road Studios for Bennett's forthcoming "Duets II" album.
Winehouse, who had struggled for years with drug and alcohol addiction, was found dead at her London home on July 23. She was 27.
The singer's father, Mitch Winehouse, said releasing the song for charity was "the most fitting tribute of all" to his daughter. Her voice sounds "as amazing and beautiful as ever" on the recording, he said. Mitch Winehouse said the foundation would fund a range of charities for young people.
The family also hopes to establish a drug rehab center for addicted youths.
"Body and Soul" will be released by Columbia Records, a division of Sony Music.