McClean, 23, who had not played an English Premier League game when Ireland beat Estonia in November to reach their first major finals in a decade, has been instrumental in Sunderland's recent climb up the table.
The Northern Ireland-born player was given a standing ovation after making his international debut in a friendly against Czech Republic in Dublin in February.
"He's young, he's physically strong and he's improved... I think he can give us energy," Trapattoni told a news conference.
McClean is unlikely to start ahead of first-choice wingers Damien Duff and Aiden McGeady but could make an impact off the bench at next month's tournament.
Wigan Athletic midfielder James McCarthy, who appeared to have come into form at just the right time, pulled out of the Irish selection process after his father was diagnosed with cancer.
Trapattoni's squad will lean heavily on the experienced trio of captain Robbie Keane, goalkeeper Shay Given and defender Richard Dunne.
All three, together with Duff, featured in Ireland's last major championship appearance 10 years ago when Spain knocked them out of the World Cup in the round of 16.
The Irish will face world and European champions Spain again next month in a tough Group C in Ukraine and Poland that also includes Italy and Croatia.
"We will look to emulate the attitude and performance that brought us qualification," said Trapattoni.
Goalkeepers: Shay Given (Aston Villa), Keiren Westwood (Sunderland), David Forde (Millwall).
Defenders: John O'Shea (Sunderland), Richard Dunne (Aston Villa), Sean St Ledger (Leicester City), Stephen Ward (Wolverhampton Wanderers), Kevin Foley (Wolverhampton Wanderers), Stephen Kelly (Fulham), Darren O'Dea (Celtic).
Midfielders: Keith Andrews (West Bromwich Albion), Glenn Whelan (Stoke City), Darron Gibson (Everton), Damien Duff (Fulham), Aiden McGeady (Spartak Moscow), Stephen Hunt (Wolverhampton Wanderers), Keith Fahey (Birmingham City), James McClean (Sunderland).
Forwards: Robbie Keane (Los Angeles Galaxy), Kevin Doyle (Wolverhampton Wanderers), Simon Cox (West Bromwich Albion), Jonathan Walters (Stoke City), Shane Long (West Bromwich Albion).
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
