The British monarch was King of England for two years from 1483 until his death in 1485 at the Battle of Bosworth Field. He was also the last King of the House of York.
He was recorded as being buried inside a Leicester church, which was later destroyed.
Team members from the University of Leicester had previously found traces of the church under a council car park, reports BBC News.
The team have now found human bones in the church's choir, the place where the King was said to have been buried.
The excavation project was launched on August 25, before the remains of the chapter house and the church were recovered.
A spokesperson from the university has confirmed that human bones were found, and that more details will be given this afternoon (September 12).
Philippa Langley of the Richard III Society said: "We came with a dream and if the dream becomes reality it will be nothing short of miraculous."
The bones will have their DNA tested against descendants of Richard III's family to discover their true identity.
Richard III has been played by the likes of Sir Laurence Olivier, Al Pacino and Sir Ian McKellen, while Peter Cook portrayed him in the first series of Blackadder.