Born in Zamość, Tytoń played for Górnik Łęczna until the end of the 2006–07 season when the Polish first-league club was relegated to the third division because of corruption. His application to be released from his contract was granted by the PZPN, following which he signed a five-year contract with Roda JC.
Roda JC
His Eredivisie debut came on 29 March 2008 in a goalless draw against Heracles Almelo. However, he did not make any appearances the following season. In January 2010, Tytoń became the club's first choice goalkeeper, taking over from Bram Castro. He had shoulder surgery at the end of March 2011. After 2010–11 Eredivisie season, Tytoń was listed as the second best goalkeeper, only behind Maarten Stekelenburg. He had an offer from Belgian champion KRC Genk, but did not accept it.
On 16 August 2011, it was announced that PSV Eindhoven had taken Tytoń on a one-year loan, with an option to buy at the end of the season. On 20 January 2012 it was announced that PSV has signed Tytoń for an extra four years. On 18 September 2011, Tytoń suffered a serious concussion when he collided with a teammate during the match between PSV and Ajax and was subsequently carried out on a stretcher, with the game delayed for 15 minutes. There was no serious damage so he was discharged from hospital the next day. In the Europa League match against FC Rapid București Tyton was back in goal for PSV. Tytoń rapidly gained a strong form in goal for PSV after his injury and replaced former first choice goalkeeper Andreas Isaksson by the time Phillip Cocu had been announced as caretaker manager after Fred Rutten in March 2012. Among many strong matches, he especially displayed his talent in the 2011–12 KNVB Beker semi final against SC Heerenveen where PSV advanced to the final on a 3–1 victory. Tytoń at times almost single-handedly kept the opposition from producing a comeback and saved a penalty from the 2011–12 Eredivise topscorerBas Dost. He followingly became known as the "Penalty Killer" among media and fans. He featured in the KNVB Beker final on 8 April 2012, where PSV beat Heracles Almelo 3–0. At the start of the 2012–13 season, Tytoń received the number 1 shirt at PSV after the departure of Isaksson. He began the season as the first choice goalkeeper, ahead of the new signing Boy Waterman. However, after five league games, Tytoń was demoted to the bench as Waterman was preferred as the first choice goalkeeper by the new manager Dick Advocaat.
On 30 June 2016, Tytoń signed a three-year deal with Deportivo de La Coruña, returning to Spain one year after leaving Elche.
FC Cincinnati
On 13 December 2018, Tytoń joined Major League Soccer side FC Cincinnati ahead of their inaugural 2019 MLS season.
International career
On 29 May 2010, he debuted for the Poland national football team in a 0–0 draw against Finland. On 11 August 2010, he played in the second half against Cameroon. He conceded two goals. Tytoń was selected in Poland's squad for UEFA Euro 2012 as a second choice goalkeeper behind Wojciech Szczęsny after Łukasz Fabiański was ruled out for the competition due to injury. On the 68th minute in the opening match against Greece, Szczęsny was given a straight red card after giving away a penalty. Tytoń came on as a substitute to replace him and saved the penalty taken by Greek captain Giorgos Karagounis. The game ended in a 1–1 draw. He became the first goalkeeper in history of the European Championships to save a penalty after coming on. After the match, Tytoń said saving the penalty was "like a dream": “It felt like a dream, I was aware that now was my chance. I really wanted to help the team. Thank God I saved the penalty.” Tytoń continued on as Poland's starting goalkeeper for the next two matches, even beyond Szczęsny's return from the red card suspension.
