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).
https://youtu.be/hCOyTzvJQvs
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.
“Daryl Braithwaite of Sherbet remade ‘You’re My World’ as his first solo recording; released in October 1974, it spent the first three weeks of 1975 at #1 on the Australian chart. ‘You’re My World’ became a Top 20 hit in the US in 1977 via the remake by Helen Reddy, introduced on her album Ear Candy. Ritchie Blackmore has been credited with playing guitar on Reddy’s recording. (Deep Purple, the group Blackmore had fronted, had been managed by Jeff Wald who in 1977 was Helen Reddy’s manager and husband.)”
Daryl Braithwaite, “You’re My World” (1974):
https://youtu.be/R0PIy6fJQOc
Helen Reddy, “You’re My World” (1977):