First recorded (in English) by Cilla Black (US #26/MOR #4/UK #1 1964).
Other hit versions by Daryl Braithwaite (AUS #1 1974), Helen Reddy (US #18 1977/MEX #1 1978).
From the wiki: “The ballad ‘You’re My World’ was originally recorded in 1963 as ‘Il Mio Mondo’ (‘My World’) by Umberto Bindi, who co-wrote the Italian-language version with Gino Paoli. Although the original Italian version was not a hit, even in Italy, the song came to the attention of UK record producer George Martin who commissioned an English-language version to be recorded by his protégée Cilla Black (‘Anyone Who Had a Heart’, ‘Alfie‘, ‘Love of the Loved‘). Black’s second consecutive #1 hit in the UK, ‘You’re My World’ would be the first track by Black to be released in the US. Peaking at #26 on the Billboard Hot 100 in 1964 (and #4 on the MOR chart), ‘You’re My World’ would be Black’s only US Top 40 hit.