The 350-bed hospital will also include 104 staff residencies, a helipad and almost 1,000 parking spaces.
Julie White, chief operating officer with NHS Dumfries and Galloway, said: “The approval by Scottish government enables us to proceed to the open market to commence our procurement process.
“We will now engage with external companies who will work with us to complete the detailed design, build the hospital and finance the construction.”
NHS Dumfries and Galloway hopes to start work in 2015 at a site near the town’s bypass at Garroch Farm.
Mott MacDonald’s Glasgow office has been signed up to provide technical and procurement advisory services throughout the project development.
Procurement is expected to get underway in the summer, but the final decision on the business case will not be known until the end of the year.
The design for the new hospital is being drawn up by architect Keppie Design.
If all goes to plan the contract to build a new Dumfries and Galloway hospital will be let in Autumn 2014.