Rickey attended the University of Oxford, studying modern history at Balliol College, and drawing and painting at the Ruskin School of Fine Art. After graduation he went to Paris, where he studied painting under Fernand Léger.
After serving in the Army Air Corps throughout World War II, Rickey studied art on the G.I. Bill, at the Institute of Fine Arts at New York University and at the Chicago Institute of Design. By the 1950s, Rickey had abandoned painting for sculpture, and had begun designing the stainless steel sculptures with moving parts that would become his specialty for the next 50 years. He died at home in St. Paul, Minnesota, in 2002, at the age of 95.
Rickey's work can be found in many private and corporate collections, as well as in major museums including the Guggenheim Museum, the Museum of Modern Art, and the Whitney Museum of American Art in New York City; the National Gallery in Washington, D.C.; the Tate Gallery in London, England; the Naoshima Contemporary Art Museum, Naoshima, Japan; The Boymans Museum in Rotterdam, the Netherlands; and the National Gallery of Scotland, in Edinburg.