The 54-year-old former England international has been out of work since resigning from his post at Reading last summer.
Coppell will replace Gary Johnson, who left Ashton Gate after five years in charge in March, although caretaker manager Keith Millen, who himself had been in the running for the post, will stay in charge for the last two games of the season.
Coppell has won promotion to the top flight three times, including setting a record haul of 106 points with Reading four years ago, and will be looking for a fourth at Ashton Gate. City have not been in the top flight for 35 years but Coppell is intent on ending that wait.
He said: "Every manager knows that promotion is his brief and I'm no different.
"This is a club that wants to go forward and wants to be in the top division. It's my opportunity to take this club there and that is our challenge.
"No one person can do it by themselves and we will need to work as a team.
"Football is a week-to-week industry and I will be looking for improvement. Everyone is judged on results and we need to win games but we need to finish strongly this season and look to kick on."
Coppell admitted that he had discussed what money would be made available to him by chairman Steve Lansdown and insisted that Millen, who is to stay on as assistant manager, will play a key part in their summer rebuilding. Coppell added: "We have obviously discussed budgets but there has not been a figure put on it. I know that the chairman has always been supportive and if I go to him he will help me bring players in.
"This club has a history in the top division and the chairman has huge ambitions for the team and the stadium."
Source: PA
Source: PA