Coppell, 54, has been out of work since the end of last season when he resigned as Reading manager following their Championship play-off semi-final loss to Burnley.
Millen had been in charge for seven matches after replacing Gary Johnson, who left by “mutual consent”. The Robins’ only loss in those games was Saturday’s 3-0 reverse against Scunthorpe.
"I'm aware this is a club who want to go forward, they want to be in the top doviosn. that's every managers ambition, it's my opportunity to take the club there," said Coppell.
"The challenge is there for next season. It's very important to try and finish this season strong as there is always a link between the results at the end of one season and the start of the next."
Millen will remain in charge of City's first-team for the final two games of the season as Coppell is unavailable due to what he described as family commitments.
Paul Sturrock has left Plymouth Argyle following the club’s relegation to League One.
Sturrock, 52, was relieved of control of the club’s first-team in December with the club stuck in a relegation battle. Sturrock, who was in his second spell as Argyle boss after also managing Southampton, Sheffield Wednesday and Swindon Town, had worked in a “business-support role” at the club but said he wanted to return to coaching.
“While I enjoyed my new role and responsibilities, I am a football manager – that is what I do,” he told Argyle’s official website.
“Argyle has been a huge part of my life and will always be close to my heart, but now is the right time to move on.”