[1] It was recorded for Dion's English-language studio album, Loved Me Back to Life (2013) and chosen as the second single in North America, most countries in Europe, Australia and New Zealand.

[6][11] The song was sent to Adult Contemporary radio stations in the United States on 24 February 2014, and the music video for "Incredible" was released on 4 June 2014.

[12][13] "Incredible" was also added to BBC Radio 2's B-List on 12 July 2014 and released as the fourth promotional single in the United Kingdom.

Andrew Hampp from Billboard wrote that the song sounds "so massive the Olympic Committee should start bookmarking it for the 2014 Winter Games".

[18] AllMusic editor Stephen Thomas Erlewine highlighted "Incredible" and called it "soulful," "modern" and "subtle" with "palpable R&B undercurrent".

[25] Caroline Sullivan from The Guardian wrote that this duet with Ne-Yo has Dion "reverting to type with a trite ballad that vows their love will 'go down in history' but 'their voices do meld soulfully.

[27] Slant Magazine's Eric Henderson noted that "Incredible" is a "power ballad that finds Dion trading lines with Ne-Yo, both singers sounding shockingly interchangeable thanks to the heavy vocal post-production".

[31][32] Thanks to Dion and Ne-Yo's performance of "Incredible" on two US television shows in mid-December 2013, The Voice and A Home for the Holidays, the song re-entered the Canadian Hot 100 at number eighty-one on 25 December 2013.

[38] On the South Korea's Gaon Music Chart, "Incredible" debuted on 14 November 2013 and peaked at number twelve in the second week.

[39] On 3 November 2013, Dion and Ne-Yo performed "Incredible" on Le Banquier in Canada to promote the album which was released two days later.

[49][50] The music video features Dion and Ne-Yo singing on a rooftop, overlooking Los Angeles interspersed with footage of real-life people showing off their incredible talents as well as a misplaced giraffe on the loose wandering around the city.