About 500 jobs will be lost in a restructure of NHS Digital across England, according to the Secretary of State for Health.
It employs about 2,700 people in IT-related roles at centres across the country, with almost 2,000 of those jobs in Leeds.
The Unison union said most of the job cuts would have to be in Leeds as "80% of NHS Digital" was based in the city.
NHS Digital said it would be offering support to affected workers.
The organisation provides information and technology help nationally to the health and social care system.
On Monday Health Secretary Matthew Hancock told Parliament: "Due to the need to reduce the size of the organisation and change the skills and capability of its workforce, NHS Digital's restructuring is planned to be delivered in a series of waves and is due to be completed by 2020/21.
"NHS Digital estimates that a net overall reduction in headcount of circa 500 full-time equivalents is expected."
All the organisation's staff are to be affected by the restructuring and would need to apply for posts in the new structure, he added.
The organisation has offices in Leeds, London, Southport, Exeter, Redditch, Washington and Southampton.
London and Exeter each has about 250 jobs and Southport just over 100, the rest of the sites are smaller.
Robert Demaine of Unison said: "It's going to be in the hundreds in Leeds, it has to be... the other offices are nowhere near as big.
"It will have an impact on the economy obviously as it is quite a large employer for the city."
The redundancy bill would be "astronomic", he added.