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.

My move has set me thinking about the future of business news.  There are two words that sum that up: global and digital.
First let us consider global. Businesses are increasingly organised so that their supply chains and markets extend across national borders. This means that events which happen in one part of the world can have important effects on businesses everywhere.
So, it is vital for business journalists to steer away from closed-economy thinking. Understanding and explaining the connections between consumers, producers, and policymakers in different countries is now essential to covering the beat.
Second, we are in the midst of a digital revolution when it comes to the way news is reported and delivered to audiences. I am not predicting that the end of TV and radio listings is right around the corner, but viewers increasingly want to watch and listen at a time when they want to.
I found this with my own programme, Talking Business with Linda Yueh, where many UK viewers watched via BBC iPlayer. Outside the UK, where the BBC's on demand service was not available, the programme had multiple showings through the week.
It is inevitable that this trend will continue. The challenge for business reporting in the digital age, though, goes beyond simply making content more easily available online to suit viewer habits.
The prevalence of social media and the internet combined with smart phones mean that people have a huge amount of information available at their fingertips. News audiences are now more informed than ever before, especially in business. When news is reported in mainstream media, for many it is no longer new.  Personally, I often find news items from social media and other online sources faster than traditional ones.
Therefore, business news should look to add value for its audience in terms of relevant and rigorous analysis rather than just the reporting of events. It should be a trusted source among the many sources of information from which the viewer can choose.
Being global and digital are what I have tried to achieve in the last two years.
This may be my last blog here. But look for my posts elsewhere on the BBC website as I will continue to pen pieces that accompany programmes as a freelance presenter.
And readers of this blog know that I will always alert them to a new post via social media.

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21 July 2015 Last updated at 20:13 BST
Planning permission was granted for the new Â£16m aerospace museum on the former Filton Airfield.
BBC reporter Charlotte Callen went on board Concorde 216 or Alpha Foxtrot as it is also known.

Alex Baptiste punished the hosts for failing to clear an early corner, prodding home from close range.
A miscued clearance from home keeper Tommy Lee allowed Che Adams to stroke the Blades' second into an empty net.
United's Ryan Flynn volleyed over, only for Billy Sharp to add a third against a Chesterfield side that remains four points above the relegation places.
Blackpool, who are in the last relegation spot, can move to within a point of the Spireites if they beat Rochdale later in the day.
Edinburgh is closer to becoming the country's first 20mph city after councillors approved plans to begin rolling out the speed limit.
[NEXT_CONCEPT]
This is my last blog here, as I've decided to leave my post as the BBC's Chief Business Correspondent based in Singapore and move back to the UK.
[NEXT_CONCEPT]
A Concorde which made its final flight back to Filton Airfield near Bristol is to be the star attraction at a new aerospace museum in South Gloucestershire.
[NEXT_CONCEPT]
Sheffield United eased to victory at the Proact Stadium to increase Chesterfield's relegation fears.