The 19-year-old, who was born in the Polish city of Konin, is a Poland Under-18 international.
He began his professional career in home country with Legia Warsaw, where he made five senior appearances during his six months with the Polish champions.
In January 2015 he made the switch to Arsenal for a fee reported to be £2.4m. He initially arrived at the Emirates Stadium as a midfielder but was soon switched to a central defensive position.
He has subsequently made two First Team appearances for the Gunners, the last of which was back in September in the EFL Cup, when Arsenal trounced Nottingham Forest 4-0.
Speaking about Bielik last August, Arsenal boss Arsene Wenger said: “He has all the qualities and ingredients to be a top-level centre-back.
"The one thing he is missing is the experience in this position because he came to us as a central midfielder, but I converted him because I felt he can play the type of football we want to play as a centre-back.”
Bielik, who will wear the number 31 shirt at Blues, will be eligible to play in Saturday's home fixture against Fulham.