Giger was born in 1940 in Chur, capital city of Graubünden, the largest and easternmost Swiss canton. His father, a pharmacist, viewed art as a "breadless profession" and strongly encouraged him to enter pharmacy, Giger recalled. He moved to Zürich in 1962, where he studied architecture and industrial design at the School of Applied Arts until 1970.
Giger's most distinctive stylistic innovation was that of a representation of human bodies and machines in a cold, interconnected relationship, he described as "biomechanical". His main influences were Painters Dado, Ernst Fuchs and Salvador Dalí. He met Salvador Dalí, to whom he was introduced by Painter Robert Venosa. Giger was also influenced by the work of the Sculptor Stanislas Szukalski, and by the Painters Austin Osman Spare and Mati Klarwein. He was also a personal friend of Timothy Leary. Giger studied interior and industrial design at the School of Commercial Art in Zurich (from 1962 to 1965) and made his first paintings as a means of art therapy.
Giger directed a number of films, including Swiss Made (1968), Tagtraum (1973), Giger's Necronomicon (1975) and Giger's Alien (1979).
Giger's first success was when H. H. Kunz, co-owner of Switzerland's first poster publishing company, printed and distributed Giger's first posters, beginning in 1969.
Giger had a relationship with Swiss Actress Li Tobler until she committed suicide in 1975. Li's image appears in many of his paintings. He married Mia Bonzanigo in 1979; they divorced a year and a half later.
Giger's style and thematic execution were influential. He was part of the special effects team that won an Academy Award for Best Achievement in Visual Effects for their design work on the film Alien. His design for the Alien was inspired by his painting Necronom IV and earned him an Oscar in 1980. His books of paintings, particularly Necronomicon and Necronomicon II (1985) and the frequent appearance of his art in Omni magazine continued his rise to international prominence. Giger was admitted to the Science Fiction and Fantasy Hall of Fame in 2013. He is also well known for artwork on several music recording albums including Danzig III: How The Gods Kill by Danzig, Brain Salad Surgery by Emerson, Lake & Palmer and Deborah Harry's KooKoo.
In 1998, Giger acquired the Château St. Germain in Gruyères, Switzerland, and it now houses the H.R. Giger Museum, a permanent repository of his work.
Giger applied his biomechanical style to interior design. One "Giger Bar" appeared in Tokyo, but the realization of his designs was a great disappointment to him, since the Japanese organization behind the venture did not wait for his final designs, and instead used Giger's rough preliminary sketches. For that reason Giger disowned the Tokyo bar. The two Giger Bars in his native Switzerland, in Gruyères and Chur, were built under Giger's close supervision and they accurately reflect his original concepts. At The Limelight in Manhattan, Giger's artwork was licensed to decorate the VIP room, the uppermost chapel of the landmarked church, but it was never intended to be a permanent installation and bore no similarity to the bars in Switzerland. The arrangement was terminated after two years when the Limelight closed. As of 2009 only the two authentic Swiss Giger Bars remain.
In addition to his awards, Giger was recognized by a variety of festivals and institutions. On the one year anniversary of his death, the Museum of Arts and Design in New York City staged the series The Unseen Cinema of HR Giger in May 2015.