The grave and evidence of a 13th Century monastery were uncovered when archaeologists were called to an Edinburgh Old Town building site.
An elaborate sandstone slab, with carvings of a Calvary Cross and ornate sword, marked the grave.
The car park was cleared to build a new Edinburgh Centre for Carbon Innovation.
As part of low carbon measures for the University of Edinburgh scheme, work was being carried out in the former car park to create a rainwater harvesting tank for the new building.
It was already known the area had been the site of the 18th Century Old High School, the 16th Century Royal High School and the 13th Century Blackfriars Monastery.
Along with the knight or nobleman's grave and skeleton, the excavation has revealed the exact location of the monastery, which was founded in 1230 by Alexander II (King of Scotland 1214-49) and destroyed during the Protestant Reformation in 1558.
Richard Lewis, the City of Edinburgh council culture convener, said it was hoped more would be found out about the remains, but the grave had already been dated to the 13th Century.
"This find has the potential to be one of the most significant and exciting archaeological discoveries in the city for many years, providing us with yet more clues as to what life was like in Medieval Edinburgh," he added.
The project's archaeological services have been provided by Edinburgh-based Headland Archaeology.
The archaeologist who found the grave, Ross Murray, had studied at the University of Edinburgh on a site only yards from where the find was made.
Mr Murray said: "We obviously knew the history of the High School Yards site while we were studying here but I never imagined I would be back here to make such an incredible discovery."