As the lead singer of the Seattle-based band Soundgarden, Chris Cornell, who has been found dead at the age of 52, had been one of the trailblazers of the city’s grunge movement in the late 1980s and 90s. Having achieved stardom with that band, he went on to further great success with Audioslave in the new millennium, while also developing a flourishing solo career. At the time of his death, Cornell was in the middle of a tour with Soundgarden, who had re-formed in 2010 after a 13-year hiatus, and had just performed at the Fox theatre in Detroit.

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The group was started in 1984 by Cornell, along with guitarist Kim Thayil and bass player Hiro Yamamoto, with Matt Cameron becoming their full-time drummer in 1986. After releasing a single, Hunted Down (1987) on the Seattle-based Sub Pop label, and a debut album, Ultramega OK (1988), for the independent SST, Yamamoto left the band, and was briefly replaced by Jason Everman, formerly of Nirvana, before Ben Shepherd joined on bass. Soundgarden signed to A&M records, and their second release for that label, Badmotorfinger (1991), became a multi-platinum seller in the US, also reaching the Top 40 in the UK. The singles from that album, Outshined and Rusty Cage, received heavy play on alternative radio stations and MTV, and Badmotorfinger earned a Grammy nomination in 1992.

An invitation to open for Guns N’ Roses on their Use Your Illusion tour (1991-93) introduced Soundgarden to huge new audiences in both the US and Europe, as did an opening slot with the heavy metal band Skid Row in 1992. “Our big moment of truth was when we were offered a slot opening up for Skid Row and we didn’t know what to do with that,” Cornell told the music journalist Pete Makowski in 2011. “Was that good or bad? And what happened was we toured with them and their audience all bought Soundgarden records.”

A berth on the 1992 Lollapalooza tour alongside Ministry, the Red Hot Chili Peppers and fellow Seattleites Pearl Jam framed Soundgarden as one of the rising names in American alternative rock. (In 1990 Cornell had joined with members of Pearl Jam to form Temple of the Dog, in tribute to the late Andy Wood of another Seattle band, Mother Love Bone. They released an eponymous album in 1991, and last year reunited for a 25th-anniversary tour.) Cornell also had a solo cameo performance in Cameron Crowe’s 1992 Seattle-based romcom Singles, with his gentle acoustic track Seasons.

Soundgarden’s next album, Superunknown (1994), duly topped the US chart (and reached No 4 in the UK), and went on to sell 5m copies in the States alone. After extensive international touring, Soundgarden started work on their fifth album, Down on the Upside, though Cornell’s desire to lighten the group’s dark, metallic sound with acoustic instruments triggered arguments with his bandmates. When it was released in 1996, it was acclaimed by reviewers but sales fell far short of its predecessor’s. After a further marathon bout of touring, the group announced they were splitting in April 1997.

Cornell released his first solo album, Euphoria Morning, in 1999. This found him exploring a mix of rock, pop and psychedelia, allowing him to use different facets of his impressive vocal range beyond a heavy-rock roar, though again critical enthusiasm did not translate into huge sales. But his solo career was put on hold when he formed Audioslave in 2001, with former Rage Against the Machine members Tom Morello, Brad Wilk and Tim Commerford, who had been recommended Cornell by the producer Rick Rubin.

Over the next five years they recorded three albums, Audioslave (2002), Out of Exile (2005) and Revelations (2006). The first of these was by far the most successful, selling 3m albums in the States and spinning off five hit singles including Cochise, Like a Stone and I Am the Highway. The release of Revelations (which reached No 2 on the US charts and 12 in Britain) was preceded by the appearance of two of its tracks, Wide Awake and Shape of Things to Come, in Michael Mann’s film Miami Vice (2006).

Cornell quit Audioslave in early 2007. This was a significant period in his career, since he had been suffering from problems with drug and alcohol abuse during his later years with Soundgarden, and had made a strenuous effort to overcome them. “It was really hard to recover from, just mentally,” he recalled. “I think Audioslave suffered from that because my feet hadn’t hit the ground yet. I was sober but I don’t think my brain was clear … It took me five years of sobriety to even get certain memories back.”

Born Christopher Boyle in Seattle, to Ed Boyle, a pharmacist, and Karen (nee Cornell), an accountant, Chris had three younger sisters and two older brothers. After his parents’ divorce, when Chris was a teenager, he and his siblings took their mother’s maiden name. He attended a Catholic elementary school, Christ the King, then Shorewood high school, but left education at 16, and worked various jobs (including sous-chef at Ray’s Boathouse restaurant).

In a 1994 Rolling Stone interview he said: “I went from being a daily drug user at 13 to having bad drug experiences and quitting drugs by the time I was 14 and then not having any friends until the time I was 16.” He eventually found his feet as a musician, and it was while performing with the Shemps, a covers band, that he met Thayil and Yamamoto, with whom he subsequently formed Soundgarden.

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In 2006, Cornell composed and recorded You Know My Name, the theme song for the James Bond movie Casino Royale. He put out his second solo effort, Carry On, in 2007, and promoted it with a campaign of touring, both in his own right and as a support act to Aerosmith.

In 2009 he released his next album, Scream, on which he collaborated with the producer Timbaland. It reached No 10 on the US album chart, Cornell’s highest solo chart placing. In 2011 he released the live album Songbook, a document of his solo acoustic Songbook tour on which he played songs from all phases of his career as well as versions of Led Zeppelin’s Thank You and John Lennon’s Imagine. “I felt like I can’t really call myself a musician or entertainer if I can’t pick up a guitar by myself and hold someone’s attention,” he explained of his decision to perform solo.

By now he was working with the reformed Soundgarden, who released the compilation Telephantasm: A Retrospective (2010). Their first new song to go public was Live to Rise, which featured in the 2012 movie The Avengers, and later that year they followed up with an album of new material, King Animal (it reached No 5 in the US and 21 in Britain). Cornell’s most recent solo album was Higher Truth (2015), a mellow, melodic work, which entered the US Top 20.

He is survived by his wife, Vicky Karayiannis, whom he married in 2004, their son, Christopher Nicholas, their daughter, Toni, and by a daughter, Lillian, from his first marriage, to Susan Silver, which ended in divorce.

• Chris Cornell (Christopher John Boyle), singer, songwriter and musician, born 20 July 1964; died 17 May 2017