University of Leicester experts stated that DNA from the bones matched the descendants of the English king's family.
The monarch was killed in the Battle of Bosworth in 1485 but the grave was lost after the church in which it was contained was demolished in the 16th century.
The skeleton was found to have suffered 10 injuries, including eight to its skull.
The bones were carbon dated to a period between 1455 to 1540, and were known to belong to a man in his late 20s or early 30s. Richard III was 32 years old when he died.
Lead archaeologist Richard Taylor said at a press conference: "Beyond reasonable doubt it's Richard. This is a historic day for Leicester."
The bones will be re-interred at Leicester Cathedral, just yards from where they were first found.
Taylor had previously said of the find: "It has been a privilege to have been involved in what could prove to be one of the biggest archaeological discoveries of recent times.
"The University of Leicester has played a pivotal role not only in leading the archaeological dig but in terms of working in partnership with the city council and the Richard III Society to bring this extraordinary project to fruition.
"It is a testament to the skill of the University of Leicester's world-class archaeological team, led by Richard Buckley, along with the meticulous scientific work of university colleagues, that has led to this moment.
"There is a palpable excitement at the university for an announcement that could potentially rewrite history."
Richard III has been played by the likes of Sir Laurence Olivier, Al Pacino and Sir Ian McKellen in the past, while Peter Cook portrayed him in the first series of Blackadder.