Members of the city council's transport and environment committee agreed on Tuesday a traffic regulation order enabling the charges.
It is now planned to introduce the 20mph network over six phases.
Phase one of the Â£2.2m project covers much of the city centre, from Queen Street to the Meadows.
Lesley Hinds, Edinburgh city council's transport convener, said: "The aim was to create safer, more attractive streets for all road users."
The limit, which will eventually cover 80% of the capital's roads. The roll out will be complete by 2018.
The scheme is designed to improve safety and encourage more people to walk or cycle.
Despite the change, speed limits on key arterial routes into the city will remain at 30 or 40mph.
About 50% of the city's roads are already 20mph.
Phase two of the project, in the north of the city, is due to begin in October.
Phase three is to start in February 2017, then phase four in June 2017, phase five in October 2017 and phase six in February 2018.
Edinburgh is closer to becoming the country's first 20mph city after councillors approved plans to begin rolling out the speed limit.