Liverpool, trailing 1-0 from the first leg, drew level just before the end of the first half through Italian midfielder Alberto Aquilani's low curling shot from inside the box.
A quiet second half set up extra time and the hosts took a 2-0 lead on the night through Yossi Benayoun's angled strike only for Forlan to smash home the ball a few minutes later.
Atletico will meet Fulham in the May 12 final in Hamburg where they will bid to win their first major European trophy since the European Cup Winners' Cup in 1962.
The Spanish side, who face Sevilla in the King's Cup next month, also reached the European Cup final in 1974.
"We have done really well," Atletico coach Quique Sanchez Flores told reporters.
"Today we got stronger as the match went on and over the two legs I think we deserved to go through.I've not known too many better moments."
For Rafa Benitez's Liverpool, Europa League silverware represented a last chance to salvage a dismal season which featured an early Champions League exit and a failed Premier League title challenge.
The hosts' inability to keep the ball up front frustrated the Liverpool fans but with halftime approaching Aquilani came to their rescue, stretching to meet Benayoun's cross and curl home a low shot.
Benitez said: "We were on top for a long time. We lost the game with a late goal but it was a good game.
"It was a pity the way they scored."
