Golding is of English and Malaysian heritage. Golding was born in Betong, Sarawak, in East Malaysia. His mother, Margaret Likan Golding, is a Malaysian of indigenous Iban ancestry. His father, Clive Golding, is English. The family lived for almost five years in Terengganu, on the east coast of Peninsular Malaysia, before moving to Surrey, England, when Henry was eight years old. There he went to The Warwick School, Redhill. He moved to Kuala Lumpur when he was 21 to pursue on-camera roles after working as a hairdresser on Sloane Street in London for a couple of years.
In March 2017, after a global casting call, it was announced that Golding would star in the film Crazy Rich Asians alongside Constance Wu. He was first brought to director Jon M. Chu's attention by accountant Lisa-Kim Ling Kuan, and Golding's charm and personality quickly won him his first acting role. Crazy Rich Asians were released in the United States and Canada on 15 August 2018 by Warner Bros. Pictures and were met with high critical praise, becoming the number one movie in U.S. and Canadian theatres over its opening weekend.
A month later, Golding appeared in Paul Feig's thriller A Simple Favor, co-starring Blake Lively, and Anna Kendrick, playing Sean, the husband of Lively's character. Following the success of Crazy Rich Asians, and, to a lesser extent, A Simple Favor, Golding was cast opposite Emilia Clarke in the romantic comedy Last Christmas, directed by Feig (in their second collaboration). Filming commenced on 26 November 2018 and continued until February 2019, and the film was released on 8 November 2019. Additionally, Golding starred alongside Matthew McConaughey, Hugh Grant, and Michelle Dockery in The Gentlemen, a 2019 crime film directed by Guy Ritchie.
He opened up about being mixed race in an interview with Bustle: "I felt like if you were an Asian mix, were you allowed to belong in any society, or were you just meant to be on the outskirts?" Golding expanded, saying, "Just because my blood I'm not full Asian doesn't mean I can't own my Asianness. And I relate so much more with my Asian side." His closeness to his Asian culture has inspired many Asians in the Hollywood industry to also embrace their roots as well and to not be afraid to show it.