The price pledge will be a welcome u-turn for customers after Whitbread boss Andy Harrison previously warned it would have to hike prices and faced a "substantial" hit as a result of the living wage announcement, made by Chancellor George Osborne in his last Budget.
The firm said that from Thursday it will increase the pay of its 12,500 baristas, including under 25s, to a minimum of £7.40 an hour once they have completed their initial training. Baristas in London will earn a minimum of £8.20 an hour.
The National Living Wage will be £7.20 an hour when it is introduced next April.
A spokesman for Whitbread said: "There have been no changes in pricing as a result of this wage rise for Costa baristas.
"We have a new menu board going up for Christmas and customers won't see any change to our prices on this."
Last week rival Starbucks unveiled plans to extend the national living wage to all of its workers, including those aged under 25, confirming that the move would not lead to price increases.
Several other big employers have also announced pay rises for staff in recent weeks ahead of the introduction of the new national living wage.
Costa managing director Chris Rogers said: "We have chosen to pay the same rates to everyone as we strongly believe that if two people are making the same contribution they should receive the same pay and that it should be linked to training and skills levels, not age."
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