Until now, only girls have been given the vaccine, which protects against cervical cancer as well as penile cancer, anal and genital cancers and some cancers of the head and neck.
Estimates from the University of Warwick suggest the vaccine, which protects against the human papilloma virus (HPV), will prevent 64,138 cervical cancers and 49,649 non-cervical cancers in the UK by 2058.
This will include 3,433 cases of penile cancer and 21,395 cases of head and neck cancer, such as throat cancer, in men.
Giving boys the jab also protects girls from HPV, which is passed on through sexual contact.
HPV causes 99% of cervical cancers as well as 90% of anal, about 70% of vaginal and vulvar cancers and more than 60% of penile cancers.
Boys will need two doses of the jab for full protection.
The first dose will be given in school in Year 8, with a follow-up dose six months to two years later, also given in school.
Dr Mary Ramsay, head of immunisation at Public Health England (PHE), said: “Offering the vaccine to boys will not only protect them but will also prevent more cases of HPV-related cancers in girls and reduce the overall burden of these cancers in both men and women in the future.
“I encourage all parents of eligible boys and girls to make sure they take up the offer for this potentially life-saving vaccine.
“It’s important not to delay vaccination, as the vaccine may be less effective as adolescents get older.”
Public health minister Seema Kennedy said: “The success of the HPV vaccine programme for girls is clear and by extending it to boys we will go a step further to help us prevent more cases of HPV-related cancer every year.
“Through our world-leading vaccination programme, we have already saved millions of lives and prevented countless cases of terrible diseases.
“Experts predict that we could be on our way toward eliminating cervical cancer for good.”
Girls in Year 8 have been offered the HPV vaccine free in school since 2008.
Figures out in December showed 83.8% of girls completed the two-dose HPV vaccination course in 2017/18, compared with 83.1% in 2016/17 and 85.1% in 2015/16.
PHE said the programme meant infections of some strains of HPV in youngsters aged 16 to 21 have fallen by 86% in England.
A Scottish study also suggested the vaccine had reduced pre-cancerous cervical disease in women by up to 71%.
Similarly, diagnoses of genital warts have declined by 90% in 15 to 17-year-old girls and by 70% in 15 to 17-year-old boys.
The HPV jab currently used by the NHS is Gardasil, which protects against HPV for at least 10 years and possibly a lifetime.
PHE said there will be no catch-up programme for older boys aged 13 to 18.
Professor Helen Stokes-Lampard, chairwoman of the Royal College of GPs, said: “The potential of this vaccine to save lives and prevent the complications of cancer is huge, and since it has been available on the NHS for girls, it has had excellent take-up, with impressive results – it’s important this success is replicated with boys.
“We’d encourage all parents of eligible children to get their child vaccinated when it is offered, and if they miss the round for any reason, that they let their school nurse know so that they can be invited to a ‘catch-up’ clinic.
“It is also important that professionals across education and health are vigilant in offering it where appropriate, and checking that children in the eligible age bracket have had their vaccination.”
Peter Baker, campaign director for HPV Action, said: “We made the case for this for five long years because we know that universal vaccination will save men’s and women’s lives, reduce suffering and in the long run save money too.”
Professor Beate Kampmann, director of the vaccine centre at the London School of Hygiene and Tropical Medicine, said: “This decision is a triumph for gender equality in cancer prevention.
“It’s pleasing to see the UK follow the example of other countries like Australia, where the vaccine has been implemented for girls since 2007 and for boys since 2013.”
The British Dental Association (BDA) warned parents to ignore “fake news” from any anti-vaccine groups suggesting injury caused by the vaccine.
It said social media “is awash” with content falsely linking the vaccine to a number of conditions.
BDA chairman Mick Armstrong said: “A universal HPV programme will offer protection to all children from life-changing conditions like throat cancer.”
More than 3,000 women in the UK are newly diagnosed with cervical cancer each year in the UK and the disease kills over 850 women annually.