Nottingham Forest midfielder Reid has not figured in the squad since the early days of Giovanni Trapattoni's reign after an incident at the team hotel after a qualifying victory over Georgia in 2008.
Stokes had been overlooked despite his exploits with Celtic, while Everton midfielder Gibson's exile was been self-imposed following Trapattoni's decision to leave him sitting on the bench for the entire Euro 2012 finals campaign in Poland.
Trapattoni, 74, lost his job after five-and-a-half years following defeats by Sweden and Austria which ended Ireland's hopes of making it to next summer's finals in Brazil.
Defenders Richard Dunne and John O'Shea, who are suspended for the game in Cologne on 11 October, will return to the squad for the clash with the Kazakhs in Dublin four days later.
Republic of Ireland squad: David Forde (Millwall), Keiren Westwood (Sunderland), Darren Randolph (Birmingham), Joey O'Brien (West Ham), Sean St Ledger (Leicester), Marc Wilson (Stoke), Seamus Coleman (Everton), Stephen Kelly (Reading), Ciaran Clark (Aston Villa), Paul McShane (Hull), Darron Gibson (Everton), Glenn Whelan (Stoke), James McCarthy (Everton), Paul Green (Leeds), Andy Reid (Nottingham Forest), Aiden McGeady (Spartak Moscow), Anthony Pilkington (Norwich), James McClean (Wigan), Robbie Brady, Stephen Quinn (both Hull), Wes Hoolahan (Norwich), Shane Long (West Brom), Robbie Keane (Los Angeles Galaxy), Jon Walters (Stoke), Kevin Doyle (Wolves), Anthony Stokes (Celtic)