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."
‘So many times when we played Manchester United, arguments would start before the first whistle had even blown – the players would try to kill each other with their eyes’ Former Arsenal star remembers famous Premier League rivalry
Bizarre Jose Mourinho statement aims to pre-empt punishment after Fenerbahce boss clashes with Galatasaray counterpart
