On 26 June 2008, Kuciak signed a three-year contract with Romanian club FC Vaslui.[1] He joined the Polish club Legia Warsaw in August 2011, later extending his contract in August 2013 until 2016.[2] In January 2013, West Ham United were reported to be in talks with him.[3] On 24 March 2014, Kuciak made his 100th appearance for Legia Warsaw in a 2–1 victory against Piast Gliwice.[4]
On 1 February 2016, Kuciak signed an 18-month contract with Hull City.[5] He debuted the same year on 23 August in the second round of EFL Cup away to Exeter City that City won 3–1.[6]