A Tesco source said higher pay rates for overtime will also be revoked in a deal agreed behind closed doors with the Union of Shop, Distributive and Allied Workers (USDAW).
But Tesco-owned garden centre chain Dobbies said it has a different pay structure and operates as a separate business so has no plans to change its pay arrangements.
USDAW confirmed that "the pay deal doesn't affect Dobbies staff".
A Tesco spokesperson said: "We have reached a positive agreement on a two-year pay and benefits package for store colleagues, which is one of the most competitive packages in the supermarket industry and is good news for the large majority of colleagues.
"We will announce details of the deal once we have spoken to colleagues about the changes. Any colleagues out of pocket from the premium changes will be given advance notice and earnings will be protected for up to two years."
Staff at discount homeware store Wilko could also see 'premiums' for working Sundays and Bank Holidays vanish from April 2016.