The Chelsea star will earn six figures for the four-part series that will chart the next generation of the Three Lions and is set to air in the spring.
A source told The Sun newspaper: "This is an exciting project for everyone.
"Amazon were desperate to land Cole. He’s one of the hottest properties in the world. The series will lift the veil on his life so far, feature exclusive footage, and help him connect with fans on a new level.
"But it won’t just be about Cole. Other England players of the future have also signed up."
Insiders say the FA gave the project the greenlight after being consulted as they showcase the lives of the players who could help the national team end a 60-year wait for a major trophy win at the 2026 World Cup.
A source added: "They know how important players like Cole will be if England are to end a 60-year wait for a major trophy.
"It’s important they allow a relationship to form between the players and fans. The FA saw the fruits of that under (Gareth) Southgate and want it to continue.
"Cole is intensely private but a balance has to be struck, given how special a talent he is. He’s excited and wants fans to get to know him. He’s just a normal kid.
"He loves football and is a whizz on Fifa in his spare time."