The limit is to be rolled out by April 2017 on all residential streets, main shopping areas, city centre streets, and roads with high levels of pedestrian and cyclist activity.
The plan follows a successful pilot in the Marchmont, Grange and Prestonfield areas of the city last year.
Transport bosses also plan to limit speeds on main roads fronted with homes and businesses to 30 mph.
Bus chiefs have backed the roll-out but voiced concerns that speed bumps should be avoided wherever possible.
This request has been largely accepted by the council, which has stated that they will not be used on those streets most likely to carry bus services.
Kim Harding, of cycle safety campaign group Pedal on Parliament, said: "This is a very positive move."