After 146 years in the business, the owners said declining tickets sales and high operating costs were to blame.
Activists who campaigned for decades against the travelling circus's animal acts welcomed the news.
The circus was well known for its hyperbolic slogan, which inspired an Oscar-winning film.
"After much evaluation and deliberation, my family and I have made the difficult business decision that Ringling Bros and Barnum & Bailey will hold its final performances in May," said a statement from Kenneth Feld, CEO of Feld Entertainment, the family business which has run the circus since the late 1960s.
However, animal rights group Peta released a statement, saying the closure "heralds the end of what has been the saddest show on earth for wild animals, and asks all other animal circuses to follow suit, as this is a sign of changing times".
In May 2016, after years of legal battles with activists, the circus stopped its elephant shows and sent the animals to live at a conservation centre in Florida.
The circus troupe, including its animals, appeared in the 1952 film The Greatest Show on Earth.
Produced by Cecil B DeMille, the film won two Oscars, including best picture.
The curtain is coming down on the most celebrated circus in the US, the "Greatest Show on Earth", run by Ringling Brothers and Barnum & Bailey.