There were tears in Paris two years ago, but tonight in Dublin there was unbridled joy for a crowd of 51,151 as a 10-year wait for a major tournament finals, and 24 for a return to the European stage, came to a joyous end.
Trapattoni is expected to be rewarded with a substantial bonus and a new two-year contract, while his players will reportedly share a €4m reward for their efforts over the campaign.
The Republic will discover who they will face in Poland and the Ukraine when the draw is made in Kiev on December 2, but in the meantime, they will celebrate a job well done after securing just their second play-off success in seven attempts by extending their unbeaten run to 11 games.
Their preparations could include a friendly against England in Dublin provided the draw does not pitch them into the same group.
Few inside or outside either camp had any real doubt that the tie was over by the time the final whistle sounded at the A Le Coq Arena on Friday night with Ireland four goals to the good and Estonia decimated by suspensions.
Tonight the green hordes turned up in force already celebrating the nation's anticipated return to the European stage.
The second leg itself could have been effectively over within the first six minutes as the Republic ripped into a reshuffled Estonian pack.
But ironically, skipper Robbie Keane, the man whose goals have been the platform for much of what his team has achieved over the last decade, passed up two glorious opportunities to add to his tally of 53.
However, keeper Pavel Londak, deputising for the suspended Sergei Pareiko blocked his effort at close range.
The striker shot instantly and instinctively, but uncharacteristically sent the ball wide of the near post to his own astonishment.
Spurred on by their early escapes, Estonia started to work their way into the game with Vassiljev, their most impressive performer in Tallinn, conducting affairs from central midfield.
However, they continued to look vulnerable at the back, and they finally succumbed 14 minutes before the break after central defender Ragnar Klavan had needlessly conceded a corner.
Trapattoni celebrated on the sidelines as the party in the stands went into full swing with qualification now assured.
Given made his first save three minutes later when he got down to claim Vladimir Voskoboinikov's skidding drive, but his evening was passing largely without incident.
The Estonians returned in determined mood and once again took the game to Ireland, although it was Ward who came closest to altering the scoreline when he forced Londak to save after cutting inside on to his right-foot from Glenn Whelan's pass.
Joel Lindpere, whose return to the international fold for the play-off had sparked such excitement, departed having made little impact with 54 minutes gone, although his side's fortunes changed markedly three minutes later.
Vassiljev picked the ball up inside the Ireland half and having made ground, smashed a 30-yard missile towards goal.
The ball dipped and swerved and although Given managed to get a hand to it, he could not keep it out as the Republic conceded just their second goal in 11 games.
Central defender Richard Dunne might have restored the home side's lead when he met Keith Andrews's clipped 67th-minute cross with a firm header, but he directed the ball straight at a grateful Londak.
Had it not been for Given, the game might have swung again with 16 minutes remaining when Martin Vunk, having seen his initial effort blocked by Glenn Whelan, unleashed a stinging drive which the Aston Villa keeper managed to turn away at full stretch.
But there was to be no further drama as the Republic qualified on home soil for the first time.