The company had already begun charging 5p for the bags, in line with legislation introduced in 2015, and this has cut the number of plastic bags the store gives out by 1.5 billion.
But Tesco says it still sells over 700 million 5p bags every year and has committed to reducing this number further.
The company will discontinue the 5p carrier bags altogether from 28 August and instead offer customers a 'Bag for Life' at a cost of 10p per bag.
The more expensive bags are made from 94% recycled plastic and will be replaced for free once they begin to wear out.
The money made from the sale of the bags will be used to fund Tesco's 'Bags of Help' scheme, which awards grants to community projects across the country.
The supermarket is also withdrawing its single-use wine carriers, and will instead lower the price of their reusable wine option from £1 to 40p.
Online customers will still be able to have their groceries delivered in single-use carrier bags at the current charge of 5p per bag.
"Today's move will help our customers use even fewer bags but ensure that those sold in our stores continue to fund thousands of community projects across the country chosen by customers.
"It's the right thing to do for the environment and for local communities."