• Cases of HPV 16 and 18 were down 83% in girls aged 15-19 - 66% in women 20-24.
• Cases of genital warts in men aged 15-19 fell by almost 50%, and also significantly in women over 30.
The success of the HPV vaccination offers hope of one day eradicating cervical cancer, say scientists who carried out a major review of evidence.
Vaccination against the human papilloma virus, which causes most cervical cancers, began over a decade ago.
A Lancet review of 65 studies covering 60 million people showed a fall in HPV cases and in pre-cancerous growths.
Over the decades, this should translate into a significant fall, and possible eradication, of cancer they said.
Jo's Cervical Cancer Trust said the data should boost faith in the jab.
What is the human papilloma virus (HPV)?
HPV is the name for a common group of viruses; there are more than 100 types of HPV.
Many women will be infected with HPV over the course of their lifetime, with no ill effect.
Most cervical cancers are caused by infection from a high-risk HPV. Others cause conditions including genital warts and cancers of the head and neck.
The vaccine, given as two injections to girls aged 12 and 13, protects against four types of HPV - 16 and 18, which are linked to more than 70% of cervical cancers - and six and 11, which cause about 90% of genital warts.
Girls who miss the HPV jab at school can still get it up to the age of 25.
Boys aged 12-13 will also be offered the jab from September this year. The vaccine does not protect against all the types of HPV that can cause cervical cancer, so women still need to go for regular screening.
There are 3,200 cases of cervical cancer and 850 deaths from the disease each year.
The review covered studies in 14 high-income countries, including the UK. They looked at HPV rates, plus cases of genital warts and pre-cancerous cells in the cervix called CIN.
It found that when rates were compared before vaccination started and eight years after:
Cases of HPV 16 and 18 were down 83% in girls aged 15-19 - 66% in women 20-24.
Genital warts cases fell 67% in girls 15-19 - 54% in women 20-24. Pre-cancerous growths were down by 51% in girls 15-19 - 31% in women 20-24. It also showed people who were not vaccinated benefited. Cases of genital warts in men aged 15-19 fell by almost 50%, and also significantly in women over 30.
Rates fell more in countries where a wider age group was vaccinated and where coverage was higher.
Public Health England principal scientist Dr David Mesher said:
"We are seeing reductions in HPV strains and in cervical disease as well, so there is every suggestion there will be reductions in cervical cancers too."
Prof Marc Brisson, from Laval University, Canada, who led the review, said: "We will see reductions in women aged 20-30 within the next 10 years."
He said cervical cancer elimination - defined as fewer than four cases per 100,000 - "might be possible if sufficiently high vaccination coverage can be achieved and maintained".
Jo's Cervical Cancer Trust said the findings "clearly showed" the impact of HPV vaccination.
"This study furthers the growing evidence to counteract those who don't believe that this vaccine works, which is now extremely encouraging," said chief executive Robert Music.
"We sincerely hope this will boost public faith in the HPV vaccine, so that more lives can be saved and we get closer to a world where cervical cancer is a thing of the past."