Biffa, which operates waste collection services in Cannock, South Staffordshire and Stafford, said completion of the deal is expected no earlier than August.
Viridor generated revenues of £85 million in 2020 stemming mostly from bin collections for local councils with a further £39 million from waste recycling and treatment facilities.
Biffa said it believes it can increase route density in line with its plan to boost collection efficiency from 2019 by a further 20 per cent by 2030.
Biffa's collections division has been growing steadily through acquisition and generated net revenues of £871 million in 2020 compared with £350 million in 2014.
CEO Michael Topham said: "When combined with the other investments we have made over the past year across waste reduction, recycling and energy recovery, we have positioned the group as a leading enabler of the UK circular economy, ready to tackle the UK's waste challenge.
"We look forward to welcoming our new colleagues from Viridor to Biffa in due course."
Biffa has been on an acquisition streak this year, buying UK surplus food and household products redistributor Company Shop Group Ltd for an upfront enterprise value of £82.5 million in February.
Viridor was sold by water utility Pennon Group PLC in July last year to funds advised by Kohlberg Kravis Roberts & Co.
Viridpor has a transfer station in Steelhouse Lane, Wolverhampton, and a collection services and glass recycling site at Tividale.