The £45m project, procured through the Health Facilities Scotland Framework, will replace the existing Princess Alexandra Eye Pavilion in the city centre, which opened in 1969.
The Scottish Government has agreed the plan and NHS Lothian and Graham Construction will now work up a full business case.
Architect NORR Consultants will design the new eye hospital, which will be located close to the Royal Infirmary on the growing Edinburgh BioQuarter campus.
The Edinburgh BioQuarter is a collaborative partnership between NHS Lothian Scottish Enterprise, University of Edinburgh and Edinburgh City Council.
Chris MacLeod, Framework Director for Graham Construction, said: “We are privileged to be working with NHS Lothian and its stakeholders in the development of the new Edinburgh eye hospital and in equipping it to offer the highest quality of care to the region and beyond for years to come.
“Graham Construction has significant experience in delivering modern healthcare facilities throughout Scotland, and we look forward to the successful completion of this important project.”