The 28-year-old former Bayern Munich custodian joins on a free transfer after spending last season at Cologne, who told Rensing he could find himself a new club this summer following their relegation to the second division.
Bayer managing director Wolfgang Holzhauser said on his club's website: "We have signed an experienced and high quality back-up for our number one Bernd Leno. We made this move as we are involved in three competitions."
Rensing, who has made more than 100 Bundesliga appearances, joined Cologne in December 2010 after being released by Bayern that summer.
Bayer sporting director Rudi Voller added: "Michael Rensing was always a key player at Cologne and he produced some outstanding performances there. His experience can and will help Bernd Leno to perform even better in goal."