The firm was selected after being pre-tendered along with Carillion and Bam Nuttall on the south of England civils framework for work values from £8m-£20m.
Skanska takes on the region from 1 August with a projects annual spend of around £30m.
The latest deal tightens Skanska grip on highway maintenance across the south of England adding to Cornwall and Devon, and Somerset.
It is also on a highways new build framework with five other firms covering Surrey, East Sussex and Kent County Council work.
Hampshire has an option to extend for a further five years past 2024 based on successful performance.
Councillor Rob Humby, Executive Member for Environment and Transport at Hampshire County Council said: “This new contract has been years in the planning. We’ve worked with councillors across all political parties, talked to other authorities, researched the market, and engaged with all potential suppliers to fully understand what they can offer Hampshire.
“I’m confident that our new contract is competitive, offers good value for money for Hampshire’s council taxpayers and can deliver the quality of work Hampshire’s residents expect and deserve.