The 30-year-old moves to the BayArena on a free transfer after less than six months with Mainz following a January switch from Lokomotiv Moscow.
Kresic served as a back-up to starting keeper Loris Karius at Mainz, failing to earn a single appearance during his short time at the Coface Arena.
And the Croatian is likely to act as a reserve at Leverkusen, who possess a talented young shot-stopper in the form of 22-year-old Bernd Leno.
However, Kresic is excited by the transfer to a side that will again be competing in the UEFA Champions League next season after reaching the last 16 this term and finishing fourth in the Bundesliga.
"Bayer Leverkusen is a great club that has always played internationally in recent years," he told the club's official website.
"It is a great challenge for me to be able to help the club achieve its goals."
