http://en.wikipedia.org/wiki/'O_Sole_Mio is the source and it has both Neopolitan and the English translation of the original lyric on.
Enter Elvis
In 1915 Charles W. Harrison recorded the first English translation of "O Sole Mio." In 1921, William E. Booth-Clibborn wrote lyrics for a hymn using the music, titled Down From His Glory. In 1949, U.S. singer Tony Martin recorded "There's No Tomorrow", which used the melody of "O Sole Mio and written by Al Hoffman, Leo Corday, and Leon Carr it charted in 1950. The recording was released by RCA Victor Records as a 78rpm record (catalog number 20-3582) and a 45rpm record (catalog number 47-3078). The record first reached the Billboard magazine charts on November 4, 1949 and lasted 27 weeks on the chart, peaking at #2. About ten years later, while stationed in Germany with the U.S. Army, Elvis Presley heard the recording, and put to tape a private version of the song, Upon his discharge, he requested that new lyrics be written especially for him, a job that was undertaken by the songwriting duo of Aaron Schroeder and Wally Gold, with a demo by David Hill. The rewritten version was titled "It's Now or Never" and was a worldwide hit for Presley.
Robert Matthew Walker in Elvis - A Study in Music comments -
" With It's Now or Never we come to one of Presley's greatest performances. This song sold around 10 million copies as a single, and is an English version of a Neapolitan song, 'O Sol Mio' . After a gentle introduction, Presley's first stirring Top E, strong and manly, sets the scene, and the ensuing singing, abetted by Floyd Cramer's graceful piano, adds to the atmosphere. The steady beat is just right and the climax, with Presley soaring up to an incredible G Sharp, is pure magic."
The original writers -
Eduardo di Capua (March 12, 1865 - October 3, 1917) was an Italian singer and songwriter. He was born in Naples, Italy in 1865. Together with the poet Giovanni Capurro, di Capua wrote the song "'O Sole Mio", which has since been recorded by many singers, both classical and popular. He also wrote "Marie Ah, Marie" (O Marie in English), another Neopolitan song. Eduardo di Capua died in 1917 in Milan, Italy. http://en.wikipedia.org/wiki/Eduardo_di_Capua
In 1898, Giovanni Capurro wrote the words to 'O Sole Mio and asked Eduardo Di Capua (who at the time was in Odessa with his orchestra-violinist father) to set it to music. The song was later presented at Piedigrotta 1898, organized by the Round Table promoted by the publisher Bideri, and came in second place after a piece called Napule Bello!. But in popular appeal, this result was quickly overturned. 'O Sole Mio became famous. Even so, it made little money for its creators.
Capurro lived in financial scarcity his entire life. An artist for art's sake, he was not concerned about receiving credit for his best-known creation. For thirty years he was associated with the newspaper Rome as a reporter, drama critic, and, late in life, as an administrative employee. Capurro was a devotee of lounges where he sang, played the piano and did amusing imitations.
Capurro died in 1920; some sources say in Naples while others say Mexico. City." http://en.wikipedia.org/wiki/Giovanni_Capurro
Writers of the Presley version
Wally Gold - Mr. Gold, who wrote songs as Wally Gold, was born in Brooklyn. After Navy service in World War II, he sang in a quartet, the Four Esquires, before becoming a songwriter. In 1960 he and his partner, Aaron Schroeder, wrote ''It's Now or Never,'' which was recorded by Elvis Presley and became a No. 1 hit. In 1963 Mr. Gold wrote ''It's My Party'' with John Gluck Jr. and Herb Wienner, and it became a best seller for Lesley Gore. Later Mr. Gold worked as a record producer.
"Aaron Schroeder was one of the key figures around the Brill Building in the 1950s and 1960s. He was a songwriter who preferred to collaborate with others, especially in improving the commerciality of a promising song. He liked to say, not entirely in jest, 'I don't read music – that's why I make so much money'.
It was with Presley that he had his greatest success, co-writing no fewer than five chart-topping hits for the singer. A Big Hunk o' Love in 1959 was followed in 1960 with Stuck on You and It's Now or Never, which Schroeder and his co-writer Wally Gold based on the Italian standard O Sole Mio. Good Luck Charm went to No 1 in 1962 and finally I Got Stung, originally a 1958 B-side, made No 1 in Britain on its re-release in 2005.
Aaron Harold Schroeder was born in Brooklyn in 1926, was a competent pianist, mostly playing by ear, who was first attracted to the big bands of the 1940s. An early success was with At a Sidewalk Penny Arcade (1948), which was recorded by both Rosemary Clooney and Guy Lombardo. In 1955, he was working as a staff writer for the publishing company Hill and Range when he learnt that they were supplying songs to Elvis Presley, who had been signed to RCA-Victor Records. Schroeder was asked to improve a song by other staff writers, I Was the One, and the result was the B-side of Heartbreak Hotel and made the US Top 20 in its own right.
While serving in the US army, Presley developed a taste for Mario Lanza's recordings and took to singing O Sole Mio for his own amusement. Presley's publisher, Freddy Bienstock, wanted a new English lyric, and Schroeder and Wally Gold wrote It's Now or Never in 30 minutes. The record, which was released in 1960, sold 20 million copies. Schroeder used his windfall to start his own label, Musicor. Whenever Schroeder was away from home, he would buy his wife, Abby, a new charm for her bracelet. This led to him and Gold composing Good Luck Charm (1962), another trans-Atlantic chart-topper for Presley." Read more here http://www.elvis.com.au/presley/aaron_schroeder_elvis_songwriter.shtml