It said the move will save 134 million plastic bags, the equivalent of 500 tonnes of plastic a year.
Waitrose and Partners said a home compostable alternative will be used for fruit and vegetable plastic bags.
The retailer said the new alternative bags will look and feel similar to the plastic ones, apart from printed text saying they are home compostable.
The material will break down in landfill if put in a normal bin and the bags can be placed in food waste caddies or home composted.
Waitrose will initially remove 5p bags from six shops from October 8, at Saxmundham, Gerrards Cross, Keynsham, Dorking, Newark and East Putney, to understand how to manage the changeover as smoothly as possible ahead of their complete removal in March 2019.
It said customers will be told before the change comes into effect in their local shop.
Earlier this year, the retailer announced it would be removing all takeaway disposable coffee cups from its shops by autumn 2018.
It said it is on target to achieve this, with cups now having been removed completely from more than 300 of its 348 shops.
It has also committed to making all its own-label packaging widely recyclable, reusable, or home compostable by 2025 and changes include a pledge not to sell any own-label food in black plastic beyond 2019.
Tor Harris, head of corporate social responsibility, health and agriculture for Waitrose, said: “The removal of these bags will change the way our customers, many of whom have been asking us to do this, shop with us in the future.
“We know we still have a lot to do, but as with our commitment to removing takeaway disposable cups earlier this year, this represents another major step forward in reducing our use of plastics.”