Biliński was born on 23 January 1988 in the city of Wroclaw. He began his senior career with Śląsk Wrocław in 2006, where he spent six seasons and took part in 26 league games.
On 3 January 2014, it was announced that Romanian side Dinamo București had reached an agreement for the transfer of Biliński,[1] signing a 2+1⁄2-year deal for €530,000.[2] In June 2015, he was released by Dinamo, a year before his contract expired.[3]