A music video to accompany the release of "Green Garden" was first released onto YouTube on 17 January 2013 at a total length of three minutes and fifty seconds. It was filmed in Southern California at Descanso Gardens in La Cañada Flintridge and the Lincoln Heights neighborhood of Los Angeles.
John Robinson of The Guardian gave the song a positive review stating:
"Laura Mvula has a voice like the Queen has a house: classy, and so big she doesn't need to use all of it at once. This very good debut single is duly a masterclass of restraint. As much as Mvula could let rip in a kind of post-Amy Winehouse retro soul sort of way, Green Garden keeps something on the bench for later: the minimal, chiming repetitions of the production and Mvula's understated Nina Simone delivery are as much the key to the song's success as the eventual gospel explosion of the chorus. She's supporting Jessie Ware soon, but one suspects she might be the one who will carry the day."
Heat gave the song four stars out of five, calling it a "soulful tune".
On 27 February 2013 the song was number 25 on the Official Chart Update. It ultimately debuted at number 32 on 3 March, moving up by one place to 31 a week later. On 28 February 2013 the song entered the Irish Singles Chart at number 77.