1996–1998: Debut album
In May 1996, Savage Garden released their debut single "I Want You" under Roadshow Music. It peaked at No. 4 on the Australian Recording Industry Association (ARIA) singles chart, while on the 1996 End of Year Singles Chart it was highest placed by an Australian artist at No. 12. On 30 September of that year they received their first ARIA award nomination, in the category Breakthrough Artist – Single, for "I Want You". The duo attended the ceremony and presented an award. Their local success drew interest from international labels and they were signed for overseas releases with Columbia Records in late November. The label's executives had Woodruff arrange for Hayes and Jones to reside in a Kings Cross hotel for 8 months, where they wrote songs for a debut album to be released in 1997. Each day the duo and Woodruff would travel to Fisher's home to plan their work. In November 1996 a second single, "To the Moon and Back", was released and reached No. 1 in January 1997 in Australia.
"I Want You" was released in North America in February 1997, where it peaked at No. 4 on the United States Billboard Hot 100 and by April had achieved gold status according to Recording Industry Association of America (RIAA). It became their first number-one hit, reaching that spot on RPM's Top 100 Singles chart in Canada in June 1997. "Truly Madly Deeply", the band's third Australian single, was released in March, which also reached No. 1 and became their signature song. Later that month, the duo's debut album, Savage Garden, entered the Australian charts at No. 1 and peaked there for a total of nineteen non-consecutive weeks.
The album was released internationally on 24 March. "I Want You" was issued across Europe in April and reached No. 11 on the United Kingdom Singles Chart, top 20 in France, New Zealand and Sweden. At the end of May, "To the Moon and Back" was the most played song on radio in the United States. In June, a fourth single, "Break Me Shake Me", was released in Australia as the album reached No. 3 on the US Billboard 200 and was certified gold by RIAA. According to rock music historian Ian McFarlane, "[It] revealed the influence of 1980s UK pop on Hayes and Jones' songwriting. Tears for Fears and Roxette melodies blended seamlessly with Eurythmics-like arrangements, while Cure-styled guitar provided the icing on the cake."
Savage Garden won a record of ten ARIA Awards in September 1997: Best Pop Release and Song of the Year for "To the Moon and Back" and Single of the Year and Highest Selling Single for "Truly Madly Deeply", Best Independent Release, Breakthrough Artist – Album, Album of the Year and Best Group for Savage Garden, Producer of the Year and Engineer of the Year for Fisher's work on that album. They followed with their fifth Australian single, "Universe" in November. "Truly Madly Deeply" became their third single in the US and replaced Elton John's "Candle in the Wind 1997", after its fourteen-week run at No. 1.
In January 1998, "All Around Me" was released as a radio-only single in Australia. 3,000 give-away copies were available at their second Brisbane concert. By the end of that year, "Truly Madly Deeply" was the most played song on US radio and became the only one-sided single to spend a year in the top 30 of the Billboard Hot 100. In November, "Santa Monica"—their final single from the album—was released exclusively in Japan, accompanied by a video of a live performance at the Hard Rock Cafe. As of 2005 Savage Garden had been certified 12× platinum in Australia, 7× platinum in the US, 3× platinum in Canada, 2× platinum in New Zealand, Singapore, and the UK.