The king died at the Battle of Bosworth in 1485 and was recorded as being buried in a Leicester church, which was later demolished.
A team from the University of Leicester has located traces of the church and it is now confirmed they have found human remains.
The bones, believed to well preserved, are undergoing DNA analysis.
As the defeated foe, Richard was given a low-key burial in the Franciscan friary of Greyfriars.
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Who was Richard III?
Richard III (reigned 1483-1485) was the last Yorkist king of England, whose death at the age of 32 in the Battle of Bosworth effectively ended the Wars of the Roses
Find out more about Richard’s reign
This was demolished in the 1530s but documents describing the burial site have survived.
The excavation, which began on 25 August, has uncovered the remains of the cloisters and chapter house, as well as the church.