The Ukrainian veteran had looked set to face former WBA champion Nikolay Valuev, but when that fight broke down on Tuesday, European champion Sosnowski stepped in and will challenge for the title.
The news is a blow to Britain's Audley Harrison, who had been due to challenge Sosnowski for the European belt in London next month.
Warsaw-born 31-year-old Sosnowski won the European title by dethroning Italian Paolo Vidoz and had previously upset Briton Danny Williams.
He unsurprisingly pulled out of the Harrison fight and said: "It's a dream come true.
"Because of the Harrison fight I am already in training and suddenly here comes the chance to fight Klitschko.
"For me, Klitschko is already over the hill. I know that I am the underdog for everybody, but I tell you, Klitschko will regret that he picked me."
Klitschko said: "I saw Sosnowski's fights on DVD and must admit that he is a very experienced, quick and tough opponent. He will do anything to get my belt but I promise that this is not going to happen."