On 23 December 2008, Załuska signed a pre-contract agreement with Celtic and would be joining at the start of the 2009–10 season. He officially became a Celtic player on 1 June 2009. He made his debut on 21 September 2009, in a 4–0 League Cup victory over Falkirk. On 25 October 2009, he made his league debut for the Hoops against Hamilton Academical as a replacement for his injured compatriot Artur Boruc and pulled off several saves in a 2–1 win. On 10 April 2010, Zaluska played in a Scottish Cup semi final for Celtic at Hampden Park which they lost 2–0 to Ross County.
At the start of the 2010–11 season Załuska became Celtic’s first choice goalkeeper after Boruc left for Italian side Fiorentina. However Celtic signed Fraser Forster on loan from Newcastle United and Załuska once again became second choice goalkeeper.
At the start of the 2011–12 season Załuska became Celtic’s first choice goalkeeper after Forster returned to Newcastle United. He started the opening SPL game against Hibernian, keeping a clean sheet in a 2–0 victory. However, Celtic’s re-signing of Forster on loan again pushed Zaluska down the pecking order. On 29 September Zaluska started in the Europa League against Udinese. Although Zaluska played well and made several good saves, the match finished 1–1 with Udinese scoring from a penalty.
After Forster was sold to Southampton, the recently acquired Craig Gordon established himself as first choice for season 2014-15. In October 2014, Załuska was injured in an apparent assault in Ashton Lane, in Glasgow’s West End. Having only made two league starts by October, Zaluska kept a clean sheet in a 1-0 league defeat of Inverness CT on 1 November 2014. Zaluska, an used substitute in the 2015 Scottish League Cup Final victory, did come off the bench in a Scottish Cup semi final defeat to Inverness on 19 April 2015. With Craig Gordon sent off in the second half for a last man challenge, Zaluska couldn’t stop the resulting penalty to make it 1-1, Celtic would go on to lose 3-2 in extra time. He next played at McDiarmid Park keeping a clean sheet with a string of fine saves in a 0-0 league draw.