This could help to control the recent outbreak of the rare virus in the UK in which 793 people have been infected so far.
The vaccine is effective against monkeypox because it is from the same family of viruses. Its use has been signed off by the vaccine experts, the Joint Committee on Vaccination and Immunisation (JCVI).
Dr Mary Ramsay, head of immunisation at UKHSA, said: "By expanding the vaccine offer to those at higher risk, we hope to break chains of transmission and help contain the outbreak.
"Although most cases are mild, severe illness can occur in some people, so it is important we use the available vaccine to target groups where spread is ongoing."
Dr Ramsay says everyone should be alert to any new spots, ulcers or blisters on any part of their body, particularly if they've had close contact with a new partner.
If you have these symptoms, the advice is to avoid close contact with others and call NHS 111 or your local sexual health centre - but call ahead first.
Robbie de Santos, from charity Stonewall said: "While we know anyone can catch monkeypox, we welcome the vaccine being offered to those gay and bi men who are eligible, who are currently at a higher risk of getting the virus.
The vaccine is already being offered to most healthcare workers caring for patients with suspected or confirmed monkeypox before being exposed, and to close contacts of confirmed cases within four days of exposure.