In 1969, it was recorded as a concept album. By then, Rice and Lloyd Webber were working on a fresh project - another concept album telling another biblical story: Jesus Christ Superstar.
That musical opened on Broadway in 1971, garnering five Tony Award nominations, and leading to, a year later, a second version on the West End. Meanwhile, Joseph had enjoyed a couple of stage productions, earned a favourable review in the Sunday Times newspaper and was ripe for further development.
"It grew out of its own steam; we were working on other projects," says Rice. "We were quite surprised by the momentum but it was a gradual thing."
By 1973, Joseph was playing on the West End and being promoted in the US as a follow-up to Jesus Christ Superstar. Rice even took to the stage, performing the role as the Pharaoh. There were various productions, some professional but most often community, throughout the 1970s and 80s.
The 1991 relaunch, with Jason Donovan in the lead role, took the musical to a whole other level of success.
"It was a much bigger production which proved it worked in big and small venues," Rice says, "but if you'd told me back in 1967 that it would still be playing around the world and in lots of different types of venues 50 years later, I would have been surprised indeed."
He gets invited to see productions of Joseph every year and reckons he's seen close to 200. He still enjoys seeing how various companies stage the musical.
Does Rice believe we're in the midst of a resurgence in musicals? No, he says, they've always been popular (his favourites are older ones such as My Fair Lady, Grease and West Side Story).
"There have been that many staggeringly good ones," he says. "I'm not sure that we're in an era where we're seeing more great musicals than in the 1970s or 80s, but the business of putting on musicals has changed."
Rice says it's easier to tour, to look over back catalogues and find ways of breathing fresh life into older productions. In the Auckland show, Earl Gregory will play the lead role of Joseph, reprising a role that thrust him on to the world stage almost a decade ago.
Since then, the award-winning South African actor has been in demand by producers around the globe. His credits include playing Seaweed in Hairspray; touring Asia as Chad in High School Musical; Dreamgirls; Rum Tum Tugger in Cats and as Anthony in Sweeney Todd.
Lowdown
What: Joseph and the Amazing Technicolor Dreamcoat
Where and when: Civic Theatre, April 15-30, then on to Wellington and Christchurch.