The research, published in The Lancet HIV journal, also found that older people are more likely to be diagnosed with advanced HIV, which is more difficult to treat.
Study author Dr Anastasia Pharris said: "We often associate HIV with younger people who are sexually active, we assume sexually active means young people.
"These findings suggest that the HIV epidemic is evolving in new directions… In the last decade, the number of cases in older people has risen, whereas in younger people it's staying stable." The study didn't look at why more older people are being infected.
Prof Janet Seeley, from the London School of Hygiene & Tropical Medicine, said: "In Europe, the USA, and Canada, increased mortality among older people living with HIV is often attributed to increased prevalence of illnesses such as cardiovascular disease, and kidney and liver failure, which can worsen HIV disease progression.
"Prevention of infection in all age groups is essential if the epidemic is to be stopped, and older age groups should not be omitted." One activist called it a "great victory", while another said she was going to buy her "dream car".