"I was flown in to lower morale over the airwaves and hopefully take people's mind's off things while they're doing this incredible job," he joked.
The show will include "an array of feel-good tunes and loads of gratitude to those working in the frontlines".
It will reach 170 hospital stations.
The Greatest Hour will be broadcast by the Hospital Broadcast Associations, and a spokesperson said: "We are thrilled James wishes to thank NHS staff in this way.
"The show will make a fantastic addition to hospital radio schedules during this difficult time."
Blunt's new single is raising funds for the NHS and World Health Organisation.