Former Barcelona and Netherlands midfielder Cocu took charge of the Rams last year after Frank Lampard's move to Chelsea.
The 50-year-old was unable to mount the desired promotion push and Derby finished 10th last season before slumping to the bottom of the table this term.
Derby had won only one of its first 11 league games this season as pressure mounted on Cocu.
Cocu missed the Rams' last game – a defeat against Barnsley – because he is currently self-isolating having been in close contact with Derby chief executive Stephen Pearce, who has tested positive for COVID-19.
Former England captain Rooney joined Derby in January as the 35-year-old looked to take his first steps into coaching while also continuing his playing carer.
After Cocu's departure, it has been suggested the ex-Manchester United striker could now be set to take over as manager.
"I am sorry that Phillip and his staff have left the club and want to thank him personally for all his help and encouragement as part of his coaching staff," Rooney said via a statement.
"The most important thing now is to stabilise the club and start moving up the table. I have been asked to be part of the coaching staff to help the team's preparations for next Saturday's [Sunday AEDT] vital match against Bristol City.
"The coaches and I will speak with the players on Monday."
Meanwhile, in a statement on Instagram, Cocu said: "I would like to take this opportunity to thank everyone at the club including the board, staff and all of the players for their fantastic support for me since arriving at Pride Park.
"Although this season has not gone as we all would have liked so far on the pitch, I believe passionately in the project that we started to build and I have no doubt that the future is bright for the club.
"Finally, I'd like to say a huge thank you to the most important people of the club, the fans."