By 1992, Unison, Celine Dion and media appearances had propelled Dion to superstardom in the North America. She had achieved one of her main objectives: wedging her way into the anglophone market and establishing fame. Apart from her rising success, there were also changes in Dion's personal life, as René Angélil would make the transition from manager to lover. However, the relationship was kept a secret as both feared that the public would find the twenty-six-year difference between their ages incongruous.
The European version of Celine Dion included "Where Does My Heart Beat Now" as a bonus track. The album was re-released on September 7, 1992 in Australia with a bonus disc containing four songs which had been previously released as singles from Unison.
The album has received varied reviews. Stephen Thomas Erlewine from Allmusic wrote that "Celine Dion's self-titled follow-up to her successful American debut is even stronger and more accomplished." Arion Berger from Entertainment Weekly commented, "She hits all the notes on Prince's graceful, desperate 'With This Tear,' but clearly she has more voice than heart." Music critic Robert Christgau called it the "Worst album of the year—that I can remember." Jan DeKnock of Chicago Tribune said that the album "is even better, because the young singer-only 24-has developed enough confidence in her second language to really deliver the emotional nuances of a lyric, especially in the ballads that dominate this album. [...] Dion has clearly joined Mariah Carey and Whitney Houston as one of the premier voices on the pop scene."
Celine Dion has sold over 5 million copies worldwide. In the United States alone, the album has sold 2,373,000 copies according to Nielsen SoundScan, and was certified 2x Platinum. It reached number 34 on the U.S. Billboard 200 chart. Dion's popularity was also showing in Canada where the album peaked at number 3 and was certified Diamond for 1 million copies sold.
In other regions of the world, Celine Dion peaked at number 15 in Australia, number 31 in New Zealand, number 59 in Japan, and number 70 in the United Kingdom. It was also certified Gold in the UK, Japan and Australia. Dion received her first World Music Award for Best Selling Canadian Female Recording Artist of the Year.