Children's heart surgery is set to resume at Leeds General Infirmary after a meeting between NHS bosses and other partners on Thursday night.
Surgery was suspended a week ago after data indicated higher-than-usual death rates at the unit.
The news worried parents in East Yorkshire, as the hospital performs complex heart surgery on young patients from the region.
Operations are due to begin early next week and Leeds Teaching Hospitals NHS Trust said work would be done to give "sufficient assurance" the unit is safe to reopen.
Data suggested death rates were double that of other centres, but the figures' accuracy has been questioned.
Doctors and other medical experts said the information had been unverified and was not fit to base a decision to close the unit on.Maggie Boyle, chief executive of the trust, said: "I am extremely confident that this service is safe and effective and should recommence at the earliest opportunity. I want partner organisations to be as confident in the service as I am."
