The Polish international had made 20 appearances in all competitions this season, but he has now opted to continue his career in the Premier League.
Jach told the club's official website: "This is a dream come true. The Premier League was the league I have followed since I was little and I always wanted to come and play here. I am very pleased and I hope that I will be able to help Crystal Palace to stay in Premier League, and perhaps achieve bigger successes.
"When I came to Zaglebie Lubin, my dream was to have a debut in the first-team. Once I achieved that I had new goals, like to regularly play in the first-team, then become a standout player. I think that at Crystal Palace I will set new goals and they will be similar.
"The first goal is to debut in the Premier League and if this happens I will fight to play on a regular basis and become part of the first-team. I know it will be difficult because the bar is set high, but I believe in myself and with hard work I can get there and achieve many successes here."
Jach could make his debut when the Eagles face West Ham United in the Premier League on January 30.