The games are to be played on April 3 and April 10. Zenit must travel to Germany for the first leg.
Zenit beat Marseille 2-0 in St Petersburg on Wednesday to make the quarter final on the away goals rule after losing 3-1 in France.
The victory was soured however by after-match allegations from Marseille of racism on the part of Zenit's fans. UEFA is currently investigating the claims.
Bayer Leverkusen were the losing finalists in the Champions league in 2002, when they lost 2-1 to Real Madrid.
Zenit's Dutch trainer, Dick Advocaat, said before the draw that he would most like to avoid another German side, Bayern Munich. While Zenit have achieved this in the quarter-final, if they defeat Leverkusen they will come up against the winner of the Bayern Munich vs Getafe (Spain) tie.
The UEFA Cup final is to be held in Manchester on May 14.
