The 24-year-old played 33 times for Barnsley last season as the Tykes secured Championship safety on the final day of the campaign.
Cywka has said that he is happy to extend his stay at Oakwell.
"I'm happy to have signed. The second half of last season showed just what we are capable of and I'm looking forward to the new season," he told the club's official website.
"The way we played when [manager] David [Flitcroft] took over, especially against the top sides and the quality we showed was the major factor in me wanting to stay here.
"I've never been part of something as crazy and special as what I experienced last season and especially the last game which gave a special feeling to what we accomplished."
Cywka has also played for Reading, Derby County and Wigan Athletic.