Calleja was born in Attard, Malta. He began singing at the age of 16, having been discovered by tenor Brian Cefai and continued his studies with Paul Asciak. At the age of 19 he made his operatic debut as Macduff in Verdi's "Macbeth" at the Astra Theatre in Gozo and went on to become a prize winner at the Belvedere Hans Gabor Competition the same year. In 1998 he won the Caruso Competition in Milan and was a prize winner in Plácido Domingo's Operalia in 1999.