The Aberdeen bypass - first approved in 2009 - has become fully operational with the opening of the final stretch of the road.
The £745m project - stretching 36 miles (58km) - has suffered a series of delays, and is now expected to cost more than £1bn.
Talks about liability over extra contractor costs are ongoing.
There has been a staggered opening since the first main bypass section opened in June last year.
The final section, which opened to traffic on Tuesday morning, is between Craibstone and Parkhill.
Transport Secretary Michael Matheson said: "This new section of the AWPR (Aberdeen Western Peripheral Route) between Parkhill and Craibstone now allows the full benefits of this transformational project to be fully realised.
"Since the major part of the road opened in December 2018, the overwhelmingly positive feedback has demonstrated the positive impact that infrastructure can bring about in people's lives."
On the issue of the dispute over costs with the contractor, he said: "They have a claim that they believe they have additional costs associated with this particular project, however, not all claims have merit.
"As it stands at the present moment, the overall cost of this project remains at the £745m that was set out at the very beginning.
"My interests are to protect the taxpayers here, to make sure that any additional costs that may be associated with the completion of this road which are the fault of the contractors or errors that they have made are costs that have to be borne by the contractors.
"Any additional claim that they have over and above that is one that has to go through a normal due process."
'Take your time'
Aberdeen and Aberdeenshire councils both welcomed the final piece of the bypass jigsaw falling into place.
Aberdeenshire Council leader Jim Gifford said: "This is the moment we've all been waiting for."
Police Scotland urged motorists to take their time to familiarise themselves with the new road.
Preparatory work for the bypass began in August 2014, and construction began in February 2015.