The last leader of the Soviet Union will join the former US president in a recorded performance of the work by the Russian National Orchestra.
The performance will be under the command of Grammy-winning conductor Kent Nagano.
"We chose former politicians who have a great ability to communicate," said Nagano.
Actress Sophia Loren will help the pair narrate the musical tale, which has been used for years in schools as a simple way to introduce children to the instuments of the orchestra.
'Wolf's story'
The three will help perform Prokofiev's tale as well as a new piece - The Wolf and Peter - which tells the tale from the wolf's point of view.
"We thought it would be interesting to see the story from the point of view of the wolf," Nagano added.
"He's in the forest but the forest is disappearing, urbanisation is cutting the trees away... and we see why the wolf is so desperate."
Mr Gorbachev is said to be particularly pleased with the environmental aspect to the piece.
He will donate the money he earns for his performance to Green Cross International - the environmental organisation he founded in 1993.
Mr Clinton is donating his fee to the International Aids Trust, whose advisory committee he chairs.
Loren and Clinton recorded their part of the narration last December in Geneva while Gorbachev is due to record his - in English - next Monday.