It is thought caretaker boss Keith Millen will remain on the coaching staff at Ashton Gate as his assistant.
City parted company with Gary Johnson in March, ending his four-year reign at the club, during which he won promotion to the Championship.
Johnson also led the club to 2007 play-off final, but his side lost 1-0 to Hull.
Coppell resigned as Reading manager at the end of last season after losing their play-off semi final to Burnley.
the dawning of a new era, a new buzz..... bring it on!
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Reading were promoted to the Premier League as champions under Coppell in 2006, collecting a record 106 points and scoring 99 goals along the way.
The Royals then ended their first season in the top flight only one place shy of a Uefa Cup spot, with Coppell earning the League Managers' Association manager of the season award for the second successive year.
As a player, Coppell had a successful eight-year spell with Manchester United and made 42 appearances for England.
Source: BBC Sport
Source: BBC Sport