The building in Fengate will be double the size of the existing facility and is expected to be running from next year.
It will replace the current centre in Dogsthorpe by summer 2018.
The majority of the new facility will have roof cover and be purpose built incorporating a former warehouse building on the council-owned site.
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A decision notice has been published to award a contract for design and build, including management of the facility for the next ten years to FCC Environment Limited.
Councillor Gavin Elsey, cabinet member for waste and street scene, said: "The new Household Recycling Centre will represent a multi-million pound investment in waste and recycling for our growing city. This is a much-needed upgrade to the current facility which is no longer fit for purpose.
"We've listened to residents about what they wanted to see in the new HRC and it will be a big improvement once it’s opened to the public. The centre is free to use, open all year and I would encourage all residents with excess rubbish, recycling or garden waste to make good use of it."
(CD)
