Contractors have re-sequenced their work in order to open up the route down The Mound and across Princes Street into Hanover Street from 5am on Saturday.
Meanwhile, the work site at the east end of Princes Street is being expanded and buses will no longer be able to use the stretch between North Bridge and South St Andrew Street.
Instead, buses between the Bridges and George Street will be diverted via Leith Street and York Place.
Council chiefs announced a new contingency plan for the top of Broughton Street which can be put into operation if traffic becomes too congested.
City council transport convener Gordon Mackenzie said arrangements following the closures of the east side of St Andrew Square and Shandwick Place at the West End earlier this year were working well.
He said: “We would like to thank the public for their continued patience while the work continues. The diversions and traffic management that was put in place in January bedded in well and every effort is being made to ensure that will also be true on this occasion.”
He added: “The on-street works are difficult for the city, businesses and travellers in particular, but the progress is evident and it’s important we build and improve on that where we can.”
From Saturday, the No 23, 27 and 45 buses will use The Mound, while buses between London Road/Elm Row and George Street will run via York Place, and the No 8 will operate via Union Street and Forth Street northbound only.
General north-south traffic through Waverley Bridge on to South St David Street will remain open.
Edinburgh taxi driver Jim Taylor said: “It’s going to make a big difference because it will give more options but I would question why it needed to be closed in the first place.”
The council said a plan had been drawn up which would restrict traffic turning right into Broughton Street from the Picardy Place roundabout in the event of heavy congestion from Leith Street.
In order to accommodate this system, the traffic flow on Forth Street will be switched from eastbound to westbound.
The next major disruption will come at the end of the month when West Maitland Street is closed for 18 months, meaning the whole stretch of road from Haymarket to Princes Street will be shut off to traffic.