The iconic Sciennes Road building, which was opened in 1895, is expected to go for tens of millions of pounds on the open market.
Property experts insisted there would be developers “queuing up” to buy the unique property, which lies in a “prime location” just off the Meadows.
The sale comes as staff at the Sick Kids Hospital prepare to move to a purpose-built, £150 million facility at Little France in spring 2018.
David Fraser, residential land and development partner at Ryden, said the sale – which is already being advertised – would attract “considerable interest”.
He said: “The Royal Hospital for Sick Children is one of Edinburgh’s most iconic properties.
“Ryden considers it a privilege to be instructed on the sale of the property and we look forward to the challenge of securing a successful sale of the site.
“We expect it to attract considerable interest from local, national and international developers as market demand for development opportunities within Edinburgh city centre is currently strong.”
Designed by George Washington Browne, the imposing building was opened on October 31, 1895 by Princess Beatrice.
The Sick Kids Hospital was previously based at Lauriston Lane, before moving to the purpose-built Meadowside House in the early 1860s.
In 2005, NHS Lothian started to develop plans to move the hospital from its present site to the Edinburgh Royal Infirmary at Little France.
The new, state-of-the-art facility was initially pegged to open in autumn 2017, but bosses announced it would be delayed by at least six months earlier this year.
They said two of the companies working on its construction had entered administration and provisional liquidation, resulting in hold-ups.
And progress was also hindered by poor winter weather and unavoidable technical construction problems.
It is thought much of the Sciennes Road site, which covers around four acres, could be developed into luxury flats.
The plot up for grabs includes the main, B-listed George Washington Browne building, 23 terraced villas and several flats located along Rillbank Terrace, Rillbank Crescent and Millerfield Place – as well as land with the potential for new-build development.
David Alexander, managing director of DJ Alexander estate agents, said: “It’s a prime location. This is a cracking site for residential development. There will be people queuing up to buy it.”
In 2001, Lothian Health Trust sold the old Royal Infirmary of Edinburgh site at Lauriston Place for £30 million.
Snapped up by a property consortium, the 20-acre plot has now been turned into the sought-after Quartermile development, with much of the David Bryce-designed infirmary buildings still visible.