It is the first signing the former Barnet and Birmingham City manager has made since taking over the Second Division club as owner, after the 18-year-old midfielder impressed The Posh with his displays as a trainee in the last year at the club.
Huke had a loan spell with non-league Kings Lynn earlier in the season and his versatility as a player made Fry move quickly to secure the teenager's services.
"We have high hopes for Shane and I am delighted to sign him on a three-year professional deal," Fry told the club's official website.
"He is a good midfielder and has done well in the reserve team for us and the experience he got at Kings Lynn was beneficial for him."
Fry, meanwhile, is hoping to secure the services of former Birmingham City midfielder Curtis Woodhouse before Friday's league clash at Bristol City.
Woodhouse was sacked by Blues after the St Andrews club believed he breached his contract by not showing up on time for pre-season training this summer.
The player has since been on trial at London Road and Fry hopes to have him signed, either on loan or permanently, by next week.
In other news, Reading's Andre Boucaud and Manchester United's Neil Wood have ended their loan spells at the club and Tony Shields is still out sorting a move to League of Ireland club St Patrick's Athletic.
Fry has warned that Shields will stay at London Road until Christmas, if his move to St Patrick's Athletic is not completed by this coming weekend.
