Selected as the lead single from the film's soundtrack in 1996, "Someday" was recorded by all–male R&B group All-4-One for the North American release, while British female R&B trio Eternal recorded their own version for the British English version of the song which received international release throughout Europe and Oceania. Mexican singer Luis Miguel recorded a Spanish version for the Latin American market, retitled "Sueña", which became a major hit. The Italian version was recorded by Neri per Caso, retitled "Quando". The youngest Celtic Woman member Chloë Agnew covered this song for her solo album called Walking in the Air and her first Celtic Woman album. The Korean version was recorded by R&B trio Solid, which was released in Korea as a bonus track of the original soundtrack album.
For the American music market, Disney enlisted R&B band All-4-One to record their own rendition of "Someday" for the film's accompanying soundtrack. While the album version of their recording was produced and arranged by William Ross, songwriter Walter Afanasieff was consulted to produce a radio mix of the song which was released by Walt Disney Records and Atlantic Records as the set's first single to US radios on June 10, 1996. The band premiered the song at the New Orleans premiere of The Hunchback of Notre Dame.
In the United Kingdom, all–female trio Eternal lent their vocals to a second version of "Someday". Produced by Simon Climie, it was first released on First Avenue on 5 August 1996 in the UK. The single became the group's eighth non-consecutive top ten entry on the UK Singles Chart and managed to reach the top thirty in Australia and Ireland. In 1997, it appeared on the trio's third studio album Before the Rain. The band performed the song for the first time in over a decade for a one-off concert put together as part of the second season of the TV series The Big Reunion.
For the Latin American music market, Disney enlisted Mexican singer Luis Miguel to record the Spanish-language rendition of "Someday" for the Latin American soundtrack. It was adapted into Spanish by Renato López, Kiko Cibrian, and Gerardo Flores. Miguel's version was included on his eleventh studio album Nada Es Igual... released in the same year. The cover peaked at number 3 on the Hot Latin Songs chart and became his fourth number one song on the Latin Pop Songs chart. A music video was filmed for Miguel's version.