"Beyond reasonable doubt it's Richard," University of Lester archaeologist Richard Buckley told a news conference, saying the remains had been subjected to "rigorous academic study."
Richard was a royal prince, the brother King Edward IV. Appointed as protector of his nephew Edward V on the king's death in 1483, Richard instead seized power.
Killed in the Battle of Bosworth after only two years on the throne, he was given a rushed burial beneath the church of Greyfriars in the center of Leicester, site of the archaeological dig that uncovered the remains.
The church was demolished during the Reformation in the 16th Century and its exact location forgotten, but historians identified the likely area and an archaeology dig was begun on the site in August 2012.
DNA from a modern ancestor of Richard's line was compared to that from the remains and found to match.
There was other evidence as well, researchers said; historians of Richard's time had portrayed him as deformed, and researchers confirmed the skeleton's spine is badly curved, a condition now called scoliosis.
"Taken as a whole, the skeletal evidence provides a highly convincing case for identification as Richard III," Leicester archaeologist Jo Appleby told the BBC.