Radamel Falcao struck twice in the first half to ease the Rojiblancos to an excellent start before Diego scored a fine individual effort late in the game to seal the victory.
The trophy win is the club's second Europa League title in three years after their victory over Fulham in 2010's final.
Diego was extremely pleased by the comprehensive victory over fellow Spanish side, acknowledging that their opponents were no pushovers and gave praise to his team mates.
“We played against a tough rival like Athletic, but we played an almost perfect match,” said Diego to Uefa’s official website, “It was a difficult match, we never said it was going to be easy. I have to thank God for this [victory].”
"It's a dream, an incredible moment."
Falcao lifted the trophy two years in a row after scoring the winning goal to win it for Porto last season.
More significantly, his brace in this match saw him retain his Golden boot title, overtaking Klaas Jan Huntellar with 12 goals in the competition this season and take his incredible overall goal tally rise to 29 goals in 29 Europa League matches.
The Colombian revelled in the joyous victory after the match, telling uefa's official website: "When I arrived at Atletico I said that I wanted to come to Bucharest and win.
"Now I thank God for this gift for this team, for my team-mates and the coaching staff. We're now looking forward to joining our fans for the celebrations back in Madrid."
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Manager Diego Simeone failed to win a continental trophy as a player with Atletico but was glad to have achieved it as a manager and was particularly happy for the Atleti fans.
"Tomorrow, when the kids go to school, they will be able to put on the shirt of Atletico Madrid with pride and this is the most wonderful thing," the former Rojiblancos midfielder told reporters after the game.
"The team performed very well and Radamel had an extraordinary match. But the credit goes to all of the players. We have been mapping the road for them but it is they who accomplish things.
"This is a great time to remember all those who have trusted in us."