The Aberdeen Western Peripheral Route (AWPR) has been subject to repeated delays, with the final section of the 36-mile dual carriageway due to have been completed in December.
Mr Matheson has now confirmed the stretch of road between Craibstone and Parkhill will open to traffic before the morning rush hour on February 19.
He thanked communities in the North East, who he said had been “extremely patient waiting for the final section of the road to be opened”.
All work on the AWPR had initially been set to be completed by spring 2018 - but the project was delayed by factors such as the weather and the collapse of construction firm Carillion.
The new road has been built under a £745 million fixed-price contract - but in December contractors told MSPs delays had resulted in hundreds of millions of pounds in additional costs, taking the overall cost to more than £1 billion.
But over the next 30 years it expected to bring an additional £6 billion to the North East economy, according to Transport Scotland.
Mr Matheson said the opening of the Parrkhill and Craibstone stretch of the road “allows the full benefits of this transformational project to be fully realised”.
He added: “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, the quality of their environment and the economy as a whole.
“The bypass was first proposed over 65 years ago but it took this Government to take the project forward in a meaningful way back in 2007.
“Despite the many challenges since then, we have taken a responsible and steadfast approach to delivering for the long-term benefit of the people and businesses of the North East.
Confirmation of the opening date comes after Aberdeen Roads Limited provided the necessary technical assurances for the River Don Crossing, which were needed before the new section of road could open.
Both Aberdeen City Council and the neighbouring Aberdeenshire Council invested £75 million in the work.