The 24-year-old will make the move to Turf Moor on a two-year-contract to boost manager Sean Dyche's options ahead of the new season.
Cisak played 59 times for Oldham in a two-year stay at Boundary Park and will now face competition from Tom Heaton for the goalkeeper's jersey, following his arrival from Bristol City.
Cisak began his career with Leicester and has also had spells with Accrington Stanley and Portsmouth.
"He is someone who wants to improve and get better and most of all wants to be number one which is imperative as we want the players to demand and challenge to be in the team and to perform," Dyche told the club's official website.
Meanwhile, striker Wes Fletcher has agreed a move to York after reaching the end of his contract at Turf Moor.