Proceeds from the single will go towards a charity being set up by Amy's father.
The track was recorded back in March at the Abbey Road Studios in London
It will be released ahead of Bennett's Duets II album, out on 20 September.
"What's going to happen is that we're putting that [Body and Soul] out ahead of the album," Bennett told MTV.
"And it's going to a foundation that her father started - to teach all the young children not to take drugs, and all the royalties of the record will go to that."
In an interview with Radio 4's Front Row last month, Bennett praised Winehouse's musical talent, calling her "truly, a good jazz singer".
Winehouse died unexpectedly, aged 27, following years of alcohol and drug addiction.
The singer's family are currently awaiting the results of toxicology tests to establish the cause of her death.
