* In 1949, he was elected to the Royal Academy of Arts in London.
* In 1951, he was awarded the Grand Prize for Sculpture at the São Paulo Art Biennial.
* In 1953, he was made a Companion of Honour.
* In 1955, he was awarded the Guggenheim International Award.
* In 1958, he was awarded the Krefeld Art Prize.
* In 1959, he was awarded the Praemium Imperiale for Sculpture.
* In 1961, he was awarded the Gold Medal of the Royal Institute of British Architects.
* In 1963, he was made a life peer, taking the title Baron Moore of Heptonstall.
* In 1970, he was awarded the Grand Prize for Sculpture at the Osaka World Expo.