The 27 year old has joined on loan until the end of the season with an option of a permanent move.
City had a £1.2million offer accepted for the Czech Republic international by the Baggies, but Bednar did not want to go to the West Country.
West Brom sporting director Dan Ashworth told skysports.com: "Bristol City made an offer for Roman that we accepted but he refused the move.
"A Turkish club came in for him for a loan and offered a decent loan fee. We preferred to sell but sometimes you have to get the best deal for the club."