Researchers who identified the king using DNA from his distant family used the same techniques to find descendants of those who fought in the battle.
They met family members directly related to the last Plantagenet king at a reception in Leicester.
Some have flown from Australia, South Africa and Canada for the occasion.
Richard, the last English king to die in battle, was killed at Bosworth Field in 1485, at the end of the Wars of the Roses.
The pro-vice chancellor at the University of Leicester, Prof Kevin Sch??rer, who conducted the research, said it was "challenging" but had "thrown up some interesting stories".
Among those identified by Prof Sch??rer are relatives whose ancestors include:
Prof Sch??rer said: "The stories are a mixture of continuity and change, with a fair measure of fame and glory thrown in.
"The inter-relation between some of the families from Bosworth is another interesting feature - in some regards it truly was a battle of cousins.
"Bringing together these families for the first time in over 500 years will be a remarkable event."
King Richard's reburial ceremony will be held at Leicester Cathedral on Thursday, led by the Archbishop of Canterbury, Justin Welby.
Descendants of some 20 families who fought at the Battle of Bosworth, that ended the reign of Richard III, have met for the first time.