Morris became a schoolteacher and moved to Wellington, where, in December 1978, the all girl group The Wide Mouthed Frogs got together to play the Artists’ Co-op. The six-piece all singing, all swinging group featured Morris on lead vocals, plus Tina Matthews (bass), Andrea Gilkison (guitar, keyboards), Sally Zwartz (drums), Katie Brockie and Sarah Mulheron. The latter two promptly retired, and were replaced by singers Callie Blood and Nicky Treadwell (keyboards). Their press release, written by Mark Cubey, noted that their show “includes various male guests, included for sex appeal, but the music is all their business, encompassing many different styles … with a visual appeal that words cannot do justice to.”

The group’s recording of ‘Some Day’ appeared on the 1979 Radio Windy compilation Homegrown alongside The Spats’ ‘Young Ladies In Hot Cars’. Spats members Fane Flaws, Bruno Lawrence, Tony Backhouse and Peter Dasent became The Crocodiles in late 1979 and set out to steal Jenny Morris from The Wide Mouth Frogs.

Morris told Jason Grech at Countdownmemories.com that ‘Tears’ was written, “to woo me into leaving the Frogs and joining the Crocodiles. Fane and Tony Backhouse would call me up at all hours to try and get me to forsake the Frogs, which I was totally against. One day they came over to my house and played this beautiful song and that’s what did it. I turned.”

The Crocodiles' single ‘Tears’ reached No.17 on the NZ Singles Chart, on April 27, 1980.

The Wide Mouthed Frogs played their farewell appearance at Radio Windy's January 1980 outdoor concert. The band’s bassist Tina Matthews also joined The Crocodiles.

The Crocodiles' single ‘Tears’ reached No.17 on the NZ Singles Chart, on April 27, 1980. The group released two albums that year – Tears and Looking At Ourselves, before headed for Australia early 1981 with a changed line-up. Lawrence, Flaws, Dasent and Matthews had departed. The group soon disbanded with drummer Barton Price joining The Models.

The debut solo single for Morris in Australia was the theme song to the movie Puberty Blues, written by Tim Finn. Sharon O’Neill sang the song in the movie but Morris released it as a single in November 1981. Morris told blogger Jason Grech, “Tim decided he wanted another version for the single.”

In 1983, now managed by Chris Murphy who also handled INXS, Morris started the group QED with Australian guitarist Rex Goh (ex-Air Supply) and NZ bassist Ian Belton. The single ‘Everywhere I Go’ got to No.21 on the Australian chart in December 1983. The album Animal Magic (EMI) was released November 1984 and produced by drummer Ricky Fataar with Mark Moffatt. It included remakes of several Crocodiles songs, plus new material written by Morris and Goh but failed to chart and the band split in 1985.

In the May 1984 issue of Rip It Up, Jenny Morris spoke of what New Zealand musicians should expect if they move to Australia: “They’ll soon find out what we all find out – you’ve got to go back to scratch. It doesn’t matter how big you are here. Dave Dobbyn’s an institution in New Zealand now but he’s a nobody over there.”

Jenny Morris had toured NZ in April 1984 with The Party Boys, an all-star line-up that included Dave Dobbyn, Mike Chunn, Peter Warren, Graham Brazier and Dave McArtney. Rip It Up (May 1984) reviewed the April 29 show at Mainstreet. Peter Thomson wrote, “The real surprise was the remarkable command of Jenny Morris. She took on songs ranging from Aretha Franklin to The Supremes and The Pretenders, sounding convincing every time. She was able to capture a dance-oriented audience with a beautifully rendered ‘Goin’ Out Of My Head’. She also sang great backup, Australia is lucky to have her.”

at the end of 1985 she embarked on the INXS ‘Listen Like Thieves’ world tour.

Morris sang backing vocals on the 1984 INXS album The Swing and at the end of 1985 she embarked on the INXS worldwide Listen Like Thieves world tour. “My whole association with INXS,” Morris noted, “Came from the fact that Michael and my best friend Michele and I were living together.”

INXS keyboard player Andrew Farris wrote and produced her September 1986 single ‘You’re Gonna Get Hurt’/ ‘Cool’ and the QED production team of Fataar and Moffatt produced the rest of her July 1987 debut album Body And Soul.  The album sold in excess of platinum (70,000) in Australia and reached No.12 on the charts. The biggest single off the album was Neil Finn’s song ‘You I Know’ that charted at No.13 in September 21, 1987. That year Morris won the ARIA Award for Best Female Performer.

In 1988 Morris married photographer Paul Clarke and for a second time, she won Best Female Artist at the ARIA Awards. Andrew Farriss was chosen to produce her second album Shiver with Morris co-writing all but one of the album’s 11 tracks. The cover song on the album was ‘(Beggar On The) Street Of Love’ by Paul Kelly. Shiver reached No.2 on the Album Sales Charts in Australia and No.6 in New Zealand, selling over 250,000 copies in Australia. The album stayed on the charts for 39 weeks in Australia and 25 weeks in New Zealand. In Australia the single ‘Saved Me’ reached No.27 in August 1989 and the very popular ‘She’s Got To Be Loved’ made it to No.5 in November 1989.

In 1990 Morris toured internationally and opened for Prince on European dates, after he heard ‘Saved Me’ in a club. In her touring band at the time was Frank Zappa’s son Dweezil on guitar. A cover of Janis Joplin’s ‘Piece Of My Heart’ charted in late 1990.

in 1991 the single ‘Break In The Weather’ made it to No.3 on the AUSTRALIAN Singles Chart.

For her next album Morris worked with producer Nick Launay and recorded in New York with the infamous Jamaican rhythm section of Sly Dunbar and Robbie Shakespeare, who anchored the classic Grace Jones recordings. The album Honeychild was released in October 1991 and reached No.4 on the Australian chart; the single ‘Break In The Weather’ made it to No.3 on the Singles Chart. The song’s video included a memorable ventriloquist’s dummy and was created by NZ-born Australian Andrew Dominik, who directed the movies Chopper and The Assassination Of Jesse James By The Coward Robert Ford.

In November 1992 Warner Music released the 16-song compilation – The Best Of Jenny Morris: The Story So Far with a re-recording of The Crocodiles hit single ‘Tears’ and ‘Jackson’, her duet with Michael Hutchence. This collaboration was previously released in April 1984, exclusively on the cassette version of the INXS EP Dekadance. The Story So Far reached No.12 on the Australian chart in April 1993.

Her next album, Salvation Jane, appeared on the rooArt label in August 1995 and featured singles ‘Only We Can Hear’ (May 1994), ‘Rhythm And Flow’ (June 1995), ‘In Too Deep’ (October 1995) and ‘What I Do Now’ (February 1996). Producers included Steve Balbi (Noiseworks, The Electric Hippies), Jeremy Allom (Massive Attack engineer), Justin Stanley and Andrew Farriss.

Jenny Morris released her next album Hit & Myth in August 2002, produced by Nick Wales on the Yep! Records label. A few months later, on Australia Day, January 26, 2003, Jenny Morris became an Australian citizen.

Morris recorded a live DVD at Sydney’s Basement venue in May 2005 with a band including included Andrew Farriss, Ian Moss, Rob Hirst (Midnight Oil) and Steve Balbi.

In June 2006, Morris released an acoustic album, Clear Blue In Stormy Skies, on Liberation Records, it featured reworked versions of earlier hits from the 1980s and 1990s along with newer material.

In January 2010, Morris received the Order of Australia for service to music and to the community through her work with the Nordoff-Robbins music-therapy charity.

Morris keeps a low profile, despite her big-selling success in Australia and New Zealand. In Rip It Up (April 1992) she knew what she wanted, “Fame doesn’t really attract me that much, I’m sort of ambivalent about it, but I do like success.”

A non-executive writer-director since 1995, in 2013 Jenny Morris was named Chair of the board of the Australasian Performing Right Association (APRA), replacing fellow New Zealander Mike Perjanik.

Morris performed her last concert at Taronga Park Zoo, Sydney, in 2014. A croakiness in her voice in recent years was diagnosed as spasmodic dysphonia (also known as laryngeal dystonia). She told the ABC in 2015, “I sound like a 50-year-old crone who's been smoking three packs a day for 30 years, and not in a good way.” 

In September 2018 it was announced Morris would be inducted into the New Zealand Music Hall of Fame at the Apra Silver Scroll. Earlier in 2018 she contributed a Songwriter's Choice column to AudioCulture, describing 10 or her favourite songs by New Zealand songwriters. In the 2019 New Year’s Honours list Jenny Morris was named a Member of the New Zealand Order of Merit for services to music and charity fundraising.