Medics are lobbying to ban sugary drinks if action is not taken by shops to reduce the sales.
Firms that have agreed to the request include WH Smith, Marks & Spencer, Greggs and Subway.
Retailers have been asked to cut sales of drinks such as fruit juices with added sugar and coffees with sugar syrup and NHS England will ask them to provide sales figures to check on progress.
'A spoonful of sugar may help the medicine go down but spoonfuls of added sugar day-in, day-out mean serious health problems, ' NHS England chief executive Simon Stevens said.
The remaining retailers are now also being urged to help "kick-start a major health drive" so the NHS "leads the way on tackling the devastating impact of the country's sweet tooth on public health".
"While this is a step in the right direction, it does not go far enough".
"It's great news that NHS England is leading by example and taking this step to make hospitals healthier places for all of us".
Shops have been told to remove salty, fatty or sugary foods from checkouts, while healthy food should be made available at all times, including to staff working night shifts.
Other targets that should be met by April 2018 include 60% of confectionery and candies in shops not exceeding 250 calories, increasing to 80% of these products in 2018/19.
As part of the new rules, 60 per cent of chocolate and candies sold in hospital shops should not exceed 250 calories, which will rise to 80 per cent in 2018; and 60 per cent of pre-packed sandwiches and meals should not contain more 400 calories by April 2018, rising to 75 per cent in 2018. She said: "We are delighted that NHS England has taken such decisive action to reduce the sale of sugary drinks in hospitals".
NHS England noted that the health service was Europe's largest employer, with over 1.3 million staff, but almost 700,000 of these are estimated to be overweight or obese.
"People with diabetes find it hard to manage their condition well in hospital".
Katherine Button, co-ordinator for Campaign for Better Hospital Food, has welcomed the move.
He added: "With this plan, people with type 1 diabetes should still have access to products that are commonly used to treat hypos".
Should the voluntary scheme secure sufficient coverage of suppliers and a subsequent reduction in sales of sugar-sweetened beverages, in early 2018 NHS England will suspend its proposed ban.