In January 2010, Mucha signed a pre-contract deal with English Premier League club Everton to join them on 1 July.

[3] Mucha made his sixth appearance for the club and his first in the 2012/13 season in a League Cup tie at home to Leyton Orient in August 2012, which Everton won 5–0.

On 2 March 2013, with regular keeper Tim Howard injured, Mucha finally made his league debut for Everton in a 3–1 home win against Reading.

[16] Mucha made his debut for Slovakia in February 2008, in a friendly match against Hungary, and became the national team's first-choice goalkeeper.

[18] He also became an occasional media pundit with public broadcaster RTVS as well as AMC Network's Sport1, especially for Slovakia national team or Slovak clubs in European competitions.