The discovery was made in Thessaloniki, Greece, in a burial ground which contained sphinxes, sculptures of caryatids and an antechamber decorated with elaborate mosaics.
The bones were located in the third room of the vast mound near Amphipolis in northern Greece, AFP reports.
They had been strewn around a rectangular wooden casket, buried under the floor of the cavernous room.
Historian Miltiade Hatzopoulos told AFP the grave is unlikely to be that of Alexander’s himself, who is believed to be buried in Alexandria, Egypt, though his remains have never been found.
Chief archaeologist Katerina Peristeri told the BBC: “The tomb in all probability belongs to a male and a general.”
In a briefing to reporters on Wednesday, the Greek Culture Ministry said: “It is an extremely expensive construction, one that no single private citizen could have funded.
“It is in all probability a monument to a mortal who was worshipped by his society at the time.”
The mystery has gripped Greece for months. Michalis Tiverios, a professor of archaeology at the University of Thessaloniki, said the human remains should provide valuable information on the occupant of the tomb, which at about 15 meters long and 4.5 meters wide is one of the biggest ever found in the country.
"It's a very important find because it will help us learn the sex of the person buried there, and possibly their approximate age," he told the AP.
Tiverios, who was not linked with the excavation, said one possible candidate would be Nearchos, one of Alexander's closest aides who led his fleet back from India to modern Iraq, and who grew up in Amphipolis.
The tomb dates back to the late 4th Century BC, when Amphipolis was a city in the Macedonian Kingdom.
Alexander started the northern Greek region of Macedonia to build an empire stretching as far as India. He died in 323 BC at the age of 32.
His generals fought over control of the empire for years, during which wars Alexander's mother, widow, son and half-brother were all murdered — most near Amphipolis.