Discovering his musical calling he studied under Arthur Barraclough in Dublin before attending the Stuttgart Conservatory for two years under Antonín Hromada in the early 1880s.
[3] He made his debut in London (at the People's Palace, Mile End) in 1888, in Handel's Messiah,[3] and in the next year appeared in Gounod's Redemption.
In April 1892 (sharing the platform with Joseph Joachim and Franz Xaver Neruda, Fanny Davies, Alfredo Piatti and Agnes Zimmermann (piano)) he sang admirably in his first set (Jean-Baptiste Lully, Peter Cornelius and Robert Schumann) in a Monday Popular Concert, but made little of his second group.
In November 1893 at the first of George Henschel's London Symphony Orchestra concerts for the season he performed Stanford's new song, "Prince Madoc's Farewell", so patriotically 'that he once or twice almost burst into the next key.'
[6] On 11 January 1895 at St James's Hall, Leonard Borwick and Greene gave the first complete public performance of Schumann's Dichterliebe to be heard in London.
Their musical partnership was still active in 1913, but the demands of their separate tours became so great by the early 1900s that they agreed not to continue their former recital programme unless it could be done wholeheartedly.
[8] He was the original baritone in the first (October 1900) performance (Birmingham Festival) of Elgar's The Dream of Gerontius, alongside Marie Brema (angel) and Edward Lloyd (soul), under Hans Richter.
At Elwes' audition for the Royal College of Music in 1903 Greene wrote to encourage him with the favourable reactions of Parry and Stanford,[11] and soon afterwards put him up for the Savile Club in London.
'[15] On 24 January 1910 he appeared in the memorial concert at Queen's Hall for August Jaeger (Elgar's 'Nimrod'), singing a group of songs by Walford Davies, and Hans Sachs's monologue from Die Meistersinger.
[16] He made his first appearance in Henry Wood's Promenade Concerts at the Queen's Hall in October 1914 singing Stanford's Songs of the Sea with the Alexandra Palace Choral Society.
[17] He had declined to fulfil an engagement to sing them there for the Stock Exchange Orchestral Society in 1907 on hearing that they still used the high English concert pitch.