Emeléus was born in Poplar, London on 22 June 1903, the son of Karl Henry Emeléus (1869–1948), a pharmacist who was born in Vaasa, Finland. The family moved to the Old Pharmacy in Battle, Sussex shortly after Emeléus was born. His elder brother Karl George Emeléus (1901–1989) went on to become professor of physics at the Queen's University of Belfast.
Emeléus was educated at St Leonards Collegiate School, Hastings, and Hastings Grammar School followed by the Royal College of Science, Imperial College, London, graduating in 1923. He gained his PhD in 1926 and a DSc three years later. During his post-graduate studies he spent time at the University of Karlsruhe as a student of  Alfred Stock and two years at Princeton University with Professor Hugh Stott Taylor. Among his many students and research colleagues, notable are Norman Greenwood, Ken McTaggart and F. Gordon A. Stone.