The song received positive reviews from contemporary music critics, although some dismissed the "simplistic" lyrical content.

In 2023, Minogue voiced a special rendition of "I Should Be So Lucky" for BBC Sport's opening film, to front England's semi-final match against Australia at the 2023 FIFA Women's World Cup.

They knew little of Minogue and had forgotten that she was arriving; as a result, they wrote "I Should Be So Lucky" in forty minutes while she waited outside the recording studio.

[3] Minogue recorded the song in less than an hour, which Stock attributes to her good ear for music and her quick memorization skills.

[4] After Minogue finished the recording session, she returned home to Australia to continue work on the soap opera, Neighbours.

[3] The track was then shelved and forgotten about by the producers, and was only mixed and completed after threats by Mushroom Records general manager Gary Ashley to fly to the UK.

[13] Hunter Felt from PopMatters gave it a positive review, stating "something about Kylie’s innocent yet forceful vocals and the sheer catchiness of the song itself [...] So the song became a beloved secret, and I never bothered to try to tune my friends in on "I Could Be So Lucky", or, crazier yet, proclaim that this "has-been" would be a critical and commercial darling in a few years time."

"[14] James Hamilton of Record Mirror called the song a "typically catchy shrill 115+1⁄2 bpm rinky tinky canterer from Stock Aitken Waterman's Bananarama reject pile", adding that "as by now everyone must be sick of hearing" Minogue.

[16] Retrospectively, in 2021, British magazine Classic Pop ranked it number 11 in their list of "Top 40 Stock Aitken Waterman songs".

[23] It was a commercial success, staying atop the Australian Kent Music Report chart for six consecutive weeks, and became her second number-one single in her home country, following "Locomotion".

[24] The single was certified platinum by the Australian Recording Industry Association (ARIA) and ranked at number five on the year-end chart for 1988.

1 hit in Finland, Germany, Hong Kong, Ireland, Israel, and Switzerland,[34][35][32] and spent seven weeks atop the South African pop chart.

[37][38] The music video for "I Should Be So Lucky" was directed by Chris Langman and filmed during November 1987 at Channel 7 Studios in Melbourne, Australia.

[39] The video features Minogue walking through her home, with scenes of her dancing in front of a colourful chalkboard background intercut throughout.

It presented a cute, wholesome, young "girl-next-door" image of Minogue to the public, with scenes of her giggling and making funny faces to the camera.

The official version of "I Should Be So Lucky" featured in the music video has been released commercially through multiple VHS and DVD collections.