The 40-year-old Scot joins the club from St Johnstone, who last week gave City permission to interview McInnes for the role.
The Saints will collect compensation reported to be in the region of ?100,000 for their boss, who emerged ahead of former Barnsley chief Mark Robins in the final reckoning.
The Ashton Gate board were said to be divided initially on which of the two they wanted in the hotseat.
But McInnes was their pick, and he will take charge of his new club for the first time when City face Birmingham on Sunday.
The managerial position at City became available after former boss Keith Millen was dismissed on October 3.
The Robins had won just once in their 10 league matches under Millen's stewardship this term, and are still to win at home in the current campaign.
The Ashton Gate board have put their faith in McInnes to arrest that trend, and he arrives at his first job in England with a glowing reputation.
Hugely respected north of the border, he took over at St Johnstone in November 2007 after his predecessor Owen Coyle joined Burnley, and 18 months later led the Saints into the Scottish Premier League for the first time in eight seasons.
Since then the former Scotland international's name has been mentioned for several vacancies in England - including those at West Brom - where he enjoyed three years as a player - and Watford before his club granted City permission to talk to him last week.
Source: PA
Source: PA