The single - entitled "Body and Soul" - was recorded back in March, and will also be released on Bennett’s “Duets II” album
on September 20.
Following the tragic death of his daughter just last month
, Mr Winehouse said that the duet would be "the most fitting tribute of all".
Earlier this week, he met with the Home Office to ask permission to open a rehabilitation
center in Amy's memory, however, this foundation is separate from that particular campaign.
Mr Winehouse said
: "We wanted to make a positive difference and help a range of causes close to Amy's heart. This could include help for children in trouble, suffering from health problems, children's hospices and more.
"While it is separate from my campaign to find more help for young addicts, that may be one of the areas the foundation contributes to.
"We intend to raise funds and distribute them to individual projects who apply for help. I couldn't be happier that everyone involved with Amy and this recording felt they wanted to contribute.
"Amy was so excited to be working with Tony Bennett and really looking forward to her fans hearing this new recording.
"The fact that Amy's voice is sounding as amazing and beautiful as ever and she is singing with the great Tony Bennett seems the most fitting tribute of all at this very difficult time."
After her post-mortem examination was inconclusive, the 27-year-old's cause of death remains unknown.