Annan met the 50-year-old musician on Thursday and told reporters afterward "he will be a peace envoy."
Ma was born in Paris to Chinese parents and was a child prodigy on the cello when he moved to the United States at the age of seven. By the time he graduated from Harvard University in 1976, he was already an internationally acclaimed cellist.
One of the most sought-after cellists in the world, Ma has won more than a dozen Grammy awards.
As a U.N. messenger of peace, Ma will join Nobel Peace Prize winner Elie Wiesel, boxing great Muhammad Ali, actor Michael Douglas, primate expert Jane Goodall and others in championing what Annan says is the world body's most urgent and important task: promoting peace.