A stunning hat-trick from former Charlton and Everton forward Ademola Lookman sealed the silverware via an immaculate performance from the Serie A side, who went into the fixture as major underdogs but rarely gave the newly-minted German champions a sniff.
Lookman became the first player to score a hat-trick in a European final for 49 years to secure Atalanta's first-ever continental trophy.
"One of the best nights of my life," Lookman told TNT Sports.
"An amazing performance from the team, we did it, we did it, we did it!
"Fantastic, third time lucky. I'm so pleased, a lot of celebrating. We made history tonight!"
The win makes them the ninth Italian club to win honours on the continent but the first to win the competition since Parma lifted the Uefa Cup in 1999.
Atalanta did so by seeing off a team that had gone 51 games unbeaten across all competitions until tonight.
The man to break the run is Gian Piero Gasperini. In charge since 2016, he is the longest-serving manager with the club from Bergamo and this trophy is his first with this side.
"I think we wrote history, also for the way we won it," the Italian coach told Uefa.com.
"It was just extraordinary, we defeated Liverpool, Sporting who won the championship. When we faced Liverpool they were first in the Premier League. And now the German champions.
"Incredible. The boys were extraordinary, a memorable performance."
Leverkusen have made a habit of late fightbacks in their remarkable run to winning a first-ever Bundesliga title without tasting defeat.
But this time they failed to dig themselves out of a hole created by a slow start.
Atalanta's more purposeful play in the opening stages was rewarded after just 12 minutes.
Davide Zappacosta got to the by-line and Lookman caught Exequiel Palacios napping to fire into the top corner at the back post.
The Nigerian has at times endured a nomadic career, bouncing around the lower reaches of the Premier League on loan spells at Fulham and Leicester after being discarded by RB Leipzig.
But Lookman has found a home in Bergamo, where he will now forever be a hero.
The 26-year-old's second goal was fit to win any final as he nutmegged Granit Xhaka before curling a powerful shot into the far corner.
For the fourth time in seven Europa League knockout matches, Xabi Alonso's men found themselves 2-0 down.
Leverkusen's flying full-backs have been at the heart of their stunning season and should have got them back in the game either side of half-time.
Alex Grimaldo fired tamely into the arms of Juan Musso before Jeremie Frimpong blazed over with the goal gaping.
Leverkusen were also denied a lifeline when Gianluca Scamacca was lucky to escape with a yellow card for a wild challenge on Florian Wirtz.
Alonso has enjoyed a rapid rise to become one of Europe's hottest coaching properties.
The Spaniard has rejected the advances of former clubs Liverpool and Bayern Munich to remain at the BayArena next season.
However, Alonso's decision to start without a recognised striker did not work and he threw on Victor Boniface at half-time to give his side a focal point up front.
Atalanta were happy to soak up the Leverkusen pressure after the break and hit on the counter-attack.
The final blow was another fabulous finish from Lookman as he skipped past Edmond Tapsoba and this time blasted into the top corner on his weaker left foot.
Dream run
Atalanta's run to the title saw them knock out some big names including Liverpool to make it to Dublin.
They topped Group D with 14 points after four wins and two draws from six games, three points ahead of Sporting.
They would face the Portuguese side again in the round of 16, and once again they saw them off with relative ease, drawing 1-1 in the first leg in Lisbon, before winning the second leg 2-1.
Their biggest test of the competition came in the quarter-finals, where they faced English giants Liverpool. The first leg at Anfield saw all of Europe sit up and pay attention to Atalanta. The Italian side won 3-0 thanks to two goals from striker Gianluca Scamacca and another from Mario Pasalic to shock Liverpool and everyone on the continent.
Liverpool did win the return match 1-0 a week later, but they could do nothing to prevent Atalanta progressing.
That second leg was the only game in the competition they had failed to score in and that run continued in the semi-finals as a brilliant performance against Marseille after a 1-1 draw in France, saw Atalanta book their spot in the final thanks to another 3-0 win.
They carried that form into the final and made history in Dublin.
A likely fifth-placed finish in Serie A, as well as the Europa League triumph, sees them back into the Champions League for the first time since 2020.
'Neverlusen' finally beaten
The incredible season of Bayer Leverkusen finally witnessed defeat, but despite their first loss in 52 games, Xabi Alonso and his players still have much to celebrate, and much still to play for.
Their 51 games unbeaten across all competitions broke the record of Benfica from the 1950s as they won their first-ever Bundesliga title in style. No defeats in 34 games was a first in the German top flight and in the process, they were able to dethrone previous 10-in-a-row winners Bayern Munich at the top of the table.
"It was not meant to be," Alonso told TNT Sports.
"We could not cope with many difficult situations that we were preparing because Atalanta demand so much of you. One-on-one situations, duels, we were not getting the ball in the right situations to take advantage. They do that so well.
"We were not able to come back and get that back. It was not meant to be.
"The unbeaten run has come to an end but congratulations to Atalanta, they deserve it, so nothing more to say."
There could yet be more domestic glory for Leverkusen on the weekend as they contest the DFB-Pokal final against second-division Kaiserslautern.
If they win that game, one where they are massive favourites, they will complete an unbeaten domestic double like few have seen in European football history.
