Campaigners had argued St Luke's at the Leicester Royal Infirmary was an important part of the city's heritage.
But the city council's planning committee voted in favour of demolition on Wednesday.
Consultant Dr Mark Ardron said he was "pleased" the Â£48m plans for the hospital had moved forward but "a bit sad" at the loss of the chapel.
A new chapel will feature "as many artefacts and fittings" from the original building as possible, he said.
"We are very pleased and relieved and just a bit sad that the historic building's got to go."
He added: "But we are very pleased we can go ahead and expand our A&E department and provide better facilities and healthcare for the people of Leicestershire."
He said the work on the new A&E department should be complete in two years.
St Luke's was built in 1887, designed by local architect William Beaumont Smith, and contains memorials to the work of doctors and nursing staff.
City councillor Adam Clarke, who stepped down from the planning department over conservation issues, said not enough thought had gone into the plans and saving the chapel.
"It was built 60 years before the NHS was founded. Nurses, patients and hospital staff have gone there to grieve, to mourn, to pray and to hope," he said.
A Victorian hospital chapel will be demolished to make way for an expanded A&E department.