The former Graveley’s fish and chip shop - now called The Fisherman’s Wife - on George Street by the market is due to close in October.
The shop, which was opened by the Stephenson family in October 1962, is set to be demolished to make way for a planned new £20m aparthotel and shops scheme on George Street.
The Fisherman’s Wife will be relocated to a unit in a new food court in Kirkgate Market.
Sandra Clarkson, 57, of Whitkirk, is the longest serving staff member and has worked at the shop for 42 years.
Assistant manager Kathryn Cosgrove, 54, of Whinmoor, has worked at the shop for 38 years and her sister, manager Linda Horsley, has worked there for 30 years.
Kathryn Cosgrove said: “It will be a sad day when we leave her.”
The late Jackson-Reed Stephenson, who died 18 months ago aged 84, ran the George Street business for more than 50 years with his wife May, 86.
Son Graham, 64, is now in charge of the business and runs five fish and chip restaurants across Yorkshire.
Graham Stephenson said the new shop is around 90 metres away from the existing one, adding: ”We have got something like 2,500 customers and I’m hoping the majority of them will walk that little bit extra to see us.”
Leeds City Council has selected property developer Town Centre Securities to deliver the new £20m scheme on George Street, next the new Victoria Gate shopping centre.
It will consist of a newly constructed building containing 117 separate aparthotel units and nine ground floor units for a range of commercial uses including retail plus cafes and restaurants and bars. Work on site is due to start next year.
Public consultation on the plans have been held this week ahead of a detailed planning application being submitted to Leeds City Council.
Alistair Smith, Associate Director at Town Centre Securities, said: “This is an exciting project that will create a new gateway to the market from George Street.
“The design will complement the recently refurbished Grade one Listed market building and regenerate George Street and the north side of the market building.”