Less than 1 percent of coffee cups are recycled in Britain, which has led to politicians calling for a "latte levy" on disposable cups.
This year it aims to recycle 100 million cups, gradually building up to 500 million a year by 2020.
The scheme has been launched in partnership with five waste collectors Veolia, Biffa, Suez, Grundon and First Mile.
Under the scheme 500m coffee cups a year would be recycled, including some sold by rivals, it said.
The plastic liners in coffee cups makes recycling hard and there are now only three sites in the UK than can process them: James Cropper in Kendall, ACE UK in Halifax, and DS Smith in Kent.
Costa sells 500 million hot drinks in disposable cups each year, a fifth of the total sold in the United Kingdom, but in the 12 months to February it collected and recycled only 14 million cups.
Internet, satellites existed in India since Mahabharat times claims Tripura CM
He was attending an event aimed at the digitization of the Public Distribution System (PDS) in Tripura. The richest culture belongs to our nation and I feel proud of it.
Costa said it would pay waste management companies 70 pounds ($100) per tonne of cups collected.
Now collectors receive £50 per tonne for cups and Costa believes that pushing that up to £120 will make it viable for them to put in place the infrastructure to process more cups.
Costa and other coffee chains do have recycling collection points for cups in their branches, but most takeaway coffees are consumed elsewhere, including in offices and on the street.
It would also continue to work with cup manufacturers to minimise and eventually eliminate plastic in takeaway cups.
Dominic Paul, managing director of Costa, told the Guardian newspaper: "By creating a market for cups as a valuable recyclable material, we are confident that we can transform the UK's ineffective and inconsistent "binfrastructure" to ensure hundreds of millions of cups get recycled every year".
In response Costa will now pay out a £90k reward to waste collection firms to retrieve cups from the general waste collection network and divert them to one of three specialist recycling centres in Cumbria, Halifax and Kent.
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