The team from the University of Leicester, working in association with the Richard III Society, is excavating a council car park in the city that they believe is the site of the friary where the Yorkist king is said to have been buried after his defeat at the Battle of Bosworth in 1485.
The dig has found remains with a "cleaved-in skull" and spinal abnormalities, which lends credence to the belief that the skeleton is that of the 15th-century royal.
A statement from the university says that an "articulated skeleton" found during excavations "is of significant interest to us".
The skeleton appears to be of an adult male that has suffered "significant peri-mortem trauma to the skull", which appears consistent with an injury received in battle, the statement says.
A "bladed implement" appears to have cleaved part of the rear of the skull and a barbed metal arrowhead was found between vertebrae of the skeleton's upper back, it adds.
"We believe the individual would have had severe scoliosis - which is a form of spinal curvature. This would have made his right shoulder appear visibly higher than the left shoulder. This is consistent with contemporary accounts of Richard's appearance," the statement says.
Leicester researchers will now test the bones for DNA against descendants of Richard III.
"The university has always been clear that any remains would need to be subjected to rigorous laboratory and DNA analysis before we confirm the outcome of the search for Richard III. We are not saying today that we have found King Richard III. What we are saying is that the search for Richard III has entered a new phase," the statement adds.
The archaeologists, known as the Time Tomb Team, have also discovered a variety of medieval artifacts during the dig.
These include a medieval silver penny and a stone frieze. Inlaid floor tiles from the cloister walk of the friary and elements of stained glass windows have also been unearthed.
Richard Taylor, director of corporate affairs at Leicester, described the findings as "truly remarkable".
Philippa Langley from the Richard III Society added: "We came with a dream and if the dream becomes reality it will be nothing short of miraculous."