The Aberdeen bypass was built under a £745m fixed-price contract, but in December 2018 Aberdeen Roads Limited, a consortium that includes Galliford Try and Balfour Beatty, told MSPs that additional costs incurred by delays had taken the overall cost to more than £1 billion.

Galliford Try’s chief executive Graham Prothero then warned in the summer that the business planned to take legal action if the final bill could not be agreed.

Transport secretary Michael Matheson, who confirmed the additional payment in a letter to MSPs on Holyrood’s rural economy and connectivity committee, said the settlement payment was “considerably less than some of the figures reported in media speculation around this dispute”.

He added: “It should also be noted that, if this settlement had not been reached, ARL would have pressed its claims through the courts.

“Whilst the Scottish ministers were prepared to mount a robust defence, it was recognised that proceedings could have run for years and led to significant and prolonged exposure to risk, expense and uncertainty as a result.

“Ultimately, all parties appreciated that an early commercial settlement was desirable in all the circumstances.”

Mr Matheson also stressed the “transformational” impact of the bypass, which fully opened to traffic in February 2019.

The AWPR was originally due to be completed by spring 2018, but its construction was delayed by factors such as the weather and the collapse of construction firm Carillion.

A Transport Scotland spokesman said: “It is important to recognise the transformational effect this project has had on people’s daily lives in the north-east, as evidenced through the widespread public support for the completed project.”