Bielik, who failed to make a single league appearance for the Gunners, is understood to have penned a five-year deal with the Rams after they agreed to pay a fee in the region of £10m.
The 21-year-old spent four-and-a-half seasons with the Gunners after making the switch from Legia Warsaw, but he was not able to command a regular role with the first-team.
While a couple of unexpected injuries hampered his progress, he was largely restricted to first-team football away from the club with the likes of Birmingham City and Charlton Athletic on loan.
He was particularly impressive with Charlton last term where he featured in both the central defensive and holding midfield positions, and he helped the Addicks seal promotion to the Championship.
Thereafter, he went on to impress for Poland at the European Under-21 Championships where he scored a couple of goals, and has now chosen a fresh challenge with Philip Cocu’s side.
Right from the beginning of the summer, Bielik was determined to pursue a move away from the north London giants, given he was frustrated playing for the reserve team.
His recent omission from the pre-season tour of United States made it clear that he was unlikely to break into Unai Emery’s side, and he now has the chance to prove himself elsewhere.
The Gunners have managed to gain four times on the £2.5m fee paid to recruit him four years ago, and that can be regarded as good business, considering he had barely featured for the club.
Hopefully, the initial £7.5m sum received from Derby goes straight into the transfer kitty for the summer, given the urgent need for a new centre-back with Laurent Koscielny aiming to push through an exit.