Dowell has moved to Pride Park on a season-long loan deal.
The 21-year-old also played in the Championship last season, helping Sheffield United to gain promotion to the Premier League.
"He is an exciting young player with a lot of potential, and I am looking forward to working with him," Cocu told Derby's official website.
Dowell's arrival follows Cocu's appointment of former Brighton and Hove Albion defender Liam Rosenior as first-team coach.
Ex-Netherlands and Barcelona midfielder Cocu was brought in by Derby when Frank Lampard took the reins with former club Chelsea after a solitary season in charge of the Rams.