The German side drew 1-1 at West Ham in the second leg of their quarter-final tie and went through 3-1 on aggregate.
Michail Antonio put West Ham ahead on 13 minutes before Jeremie Frimpong leveled in the 89th minute for Xabi Alonso's side.
Leverkusen will face Roma for a place in the final.
"I think we felt it in the first half, for me, it was a typical English crowd. They were pushing West Ham unbelievably. We were lucky in the first half if we're honest," Leverkusen midfielder Granit Xhaka told TNT Sports.
"It was a different phase in the second half, we controlled the game. We are happy we got through.
"We competed much more. If you see over 180 minutes, the better team go through."
Last weekend, Leverkusen won the Bundesliga for the first time, ending Bayern Munich's 11-year grip on the title.
They remain in contention for a treble trophy haul this season as they also face second-division Kaiserslautern in the German Cup final on May 25.