By Genevieve Hassan
Zac Efron, Vanessa Hudgens, Ashley Tisdale and Corbin Bleu were joined by dancers and basketball players on the red carpet.
Hudgens said she was "amazed" by the number of fans that turned out to see the cast make their appearance.
The film will be released in cinemas across the UK on 22 October.
Corbin Bleu on the red carpet"We came here for the first premiere, so coming back and seeing how many more people came and how much of a bigger deal it is, is amazing," Hudgens told the BBC News website.
The BBC's Colin Paterson said you could "almost smell the hormones" in Leicester Square, as young fans turned out to see 20-year-old heartthrob Efron - who plays basketball player Troy Bolton in the film series.
"For noise levels, this ranks up there with the screams for Johnny Depp at the Pirates of the Caribbean premiere," our correspondent said.
High School Musical 3 follows the pressures of being in the final year of high school before going off to college.
Fans will also get to see how the two lead characters' romance blossoms, following their first on-screen kiss at the end of High School Musical 2.
Efron: 'Why I love High School Musical'
"I've always admired that about them, it builds up the tension and finally in High School Musical 3 it feels well deserved," said Efron.
"It's about time - we're seniors, we're adults," he said.
Hudgens, who stars as maths whizz and love interest Gabriella Montez, added: "It just shows their respect for each other - it's a really sweet and innocent love that doesn't need everything else."
The film also introduces British teen actress Jemma McKenzie-Brown as a new character, Tiara Gold.
"I had a fantastic time - they welcomed me into the cast right away," the 13-year-old told the BBC News website.
Co-stars Ashley Tisdale and Corbin Bleu both said they were sad to see the end of their High School Musical journey.
"It's hard because we love working together and this project is the last chapter for us, but I'm excited to see what the future holds," Tisdale said.
Vanessa Hudgens talks about the movie
Bleu added: "It was sad to move away from the halls of East High but it's good to be able to graduate and move on to some new projects."
But with all the cast dodging questions on whether reports of a fourth instalment are true, director Kenny Ortega said he remained hopeful.
"If these kids are still reacting this way after High School Musical 3, I think it would be fun to try to imagine how we would do it for the next generation," he said.
This is the first cinematic release for the series - the first two instalments were made-for-TV movies which were initially screened on the Disney Channel. Cinemas have already taken record advance bookings.
The original TV movie took the US by storm in January 2006.
It went on to become a worldwide phenomenon and its sequel shattered cable TV records last summer, with 18.6m people in the US tuning in for its premiere.
The Disney franchise has spawned a top-selling soundtrack album and a 40-date tour of the US, not to mention countless school productions.
7 months ago