Hamer’s 57th-minute strike clinched Coventry’s 1-0 aggregate victory in the semi-final second leg at the Riverside Stadium.
Mark Robins’ side head to Wembley on May 27 bidding for a return to the Premier League for the first time since 2001.
Luton, looking to reach the top-flight for the first time since 1992, beat Sunderland 2-0 to earn a 3-2 aggregate success in their semi-final second leg on Tuesday.
Coventry finished fifth in the Championship, while third placed Luton were 10 points ahead of them.
While Coventry, FA Cup winners in 1987, can look forward to making more history for their club at Wembley, Middlesbrough will spend a seventh year in the second tier.
It was a frustrating end to former Manchester United star Michael Carrick’s impressive first year as a manager.
Coventry gradually worked their way into the game and Kyle McFadzean headed over from Hamer’s 17th-minute cross.
Sky Blues defender Jake Bidwell bravely blocked Marcus Forss’ shot from Matt Giles’ cross five minutes before the break, while Darragh Lenihan headed an Alex Mowatt corner straight at Ben Wilson.
It was the visitors who forced their way in front when Ben Sheaf pounced on Giles’ loose pass to find Viktor Gyokeres, who evaded Zack Steffen’s challenge before Hamer took over, stepped inside Forss and fired into the top corner.
Hamer might have doubled his tally with 15 minutes remaining, but saw his free-kick crash back off the crossbar with Steffen beaten.
Middlesbrough substitute Matt Crooks had the ball in the net in a tense finale, but Coventry were saved by an offside flag that sent them into the final.
