Kelly's international future had been in doubt after public criticism of Trapattoni who questioned the Reading fullback's commitment to the Irish team when he missed a friendly against Poland in February.
Veteran centre-back Richard Dunne, who has not played since Euro 2012, is still on the injury list but Trapattoni has welcomed back Everton's Seamus Coleman and Stoke's Marc Wilson to the squad.
Ireland, third in qualifying Group C, face Sweden away on March 22 and Austria at home four days later.
Goalkeepers - Keiren Westwood (Sunderland), David Forde (Millwall), Darren Randolph (Motherwell FC)
Defenders: John O'Shea (Sunderland), Sean St Ledger (Leicester City), Ciaran Clark (Aston Villa), Marc Wilson (Stoke), Seamus Coleman (Everton), Stephen Kelly (Reading), Darren O'Dea (Toronto), Joey O'Brien (West Ham), Paul McShane (Hull City), Alex Pearce (Reading), Stephen Ward (Wolverhampton Wanderers)
Midfielders - Glenn Whelan (Stoke City), James McCarthy (Wigan Athletic), Paul Green (Leeds United), Jeff Hendrick (Derby County), Aiden McGeady (Spartak Moscow), Anthony Pilkington (Norwich City), James McClean (Sunderland), Robbie Brady (Hull City)
Forwards - Robbie Keane (LA Galaxy), Kevin Doyle (Wolverhampton Wanderers), Shane Long (West Bromwich Albion) Simon Cox (Nottingham Forest), Jonathan Walters (Stoke City), Conor Sammon (Derby County), Wes Hoolahan (Norwich City).
- Sports & Recreation
- Seamus Coleman
- Marc Wilson