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.

[citation needed] 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.

[4] 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.

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.

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.

[16] On 30 June 2016, Tytoń signed a three-year deal with Deportivo de La Coruña, returning to Spain one year after leaving Elche.

[17] He started the season as a backup to Germán Lux, but due to the team's poor defensive performances, Tytoń took over as the starter on 31 October in a 1–1 draw against Valencia.

[18] The club finished in 16th place; clear of relegation, and Tytoń made 13 total appearances during the season, losing his starting spot to Lux again after poor displays against Barcelona (4–0) and Celta (4–1).

[24] On 7 March 2022, Tytoń returned to the Eredivisie to play for AFC Ajax who were in desperate need of a goalkeeper after injuries of Maarten Stekelenburg, Remko Pasveer and Jay Gorter.

[29] On the 68th minute in the opening UEFA Euro 2012 match against Greece, Tytoń came on as a substitute to replace Maciej Rybus and saved the penalty taken by Greek captain Giorgos Karagounis.