The eight-year contract, worth £4.7m a year, will begin in November 2019, with Biffa vowing to work with current provider Veolia to ensure a smooth transition.
It will include street cleaning and have an option to extended for a further two terms.
Veolia has been Waverly Borough Council’s waste collector for 14 years.
Biffa will review collection rounds and may make collection day changes once the contract begins.
New vehicles will be brought in to add textile and small WEEE kerbside recycling to the existing refuse, recycling, food, clinical and green waste collections.
Councillor Andrew Bolton, portfolio holder for environment at Waverley Borough Council, said: “The contract is comparable to what we are currently paying and is the single largest council contract awarded. We are delighted that we can work with Biffa.”