The application has been submitted for the first phase of the project, which includes a £48m state-of-the-art facility to provide acute mental health care for patients.
It would also house an intensive psychiatric care unit and a specialist brain injury unit.
It is anticipated that the first phase of the scheme would be completed by 2017, but the project as a whole could take up to 10 years to complete.
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David Small, Chairman of the Royal Edinburgh Hospital project board at NHS Lothian, is quoted by the BBC as saying: "We have worked closely with a number of interested parties, including, staff, patients and members of the local community, and a great deal of effort has gone into reaching this momentous stage.
"We await the outcome with anticipation. The public consultation has been extremely helpful in informing us, going forward on key elements of the redevelopment.
"We have listened to what matters to people and are confident that the plans will deliver an excellent mental health facility that will open a new chapter in the hospital's proud 200-year history, being celebrated this year."
The hospital, which first opened in 1813, currently provides acute psychiatric and mental health care, including the treatment of those with learning difficulties and dementia. It also offers specialist services for the treatment of eating disorders, alcohol problems and young people with mental health problems.
(JP/CD)
