Ministers initially withdrew funding for a replacement for the hospital, which treats patients across southeast Scotland, before pledging to support it in the run-up to May’s Holyrood election.
The Eye Pavilion, which opened in 1969, was deemed no longer fit for purpose by NHS Lothian earlier this year - with patients facing lengthy delays for treatment.
Campaigners are worried that its services could be split up across the region if a replacement is not funded.
Health Secretary Humza Yousaf said he was “delighted” that the outline proposal had been approved.
“The Scottish Government is committed to working closely with NHS Lothian to meet the demand for eye care, with improvements for patients and a more modernised service,” he said.
Calum Campbell, Chief Executive of NHS Lothian, also welcomed the news.
He said: “We are pleased that the Outline Business Case for the Eye Pavilion has been approved by Scottish Government.
“This brings us a step closer to making the vision for a replacement eye hospital a reality.
“We are dedicated to improving vital services for patients and a lot of work has gone into the project so far. I would like to thank all of the teams involved.
“There is still much left to do, however, and we will continue to work with our clinical colleagues as we prepare the Full Business Case.”
NHS Lothian has now been asked to submit a full business case.
A new Eye Pavilion, if approved, will be part of a £10 billion Scottish Government investment in the NHS’s estate over the next 10 years.
In May, the Keep Edinburgh Eye Pavilion (KEEP) campaign group called for a new facility to be built in Little France’s BioQuarter, a site it argued was easy to access for patients, and where research and technical innovation would be encouraged.
The latest development comes after NHS Lothian was ordered by ministers to carry out a review of its eye care services - including the ways patients were helped to access care closer to their homes.