An increasing number of people are being discouraged from seeking vital health services for fear of attacks and punishment, they added.
President Yoweri Museveni signed the Anti-Homosexuality Bill into law after parliament watered it down.
It is still among the harshest anti-LGBTQ laws in the world.
Homosexual acts are already illegal in Uganda but now anyone convicted faces life imprisonment.
The legislation imposes the death penalty for so-called aggravated cases, which include having gay sex with someone below the age of 18 or where someone is infected with a life-long illness including HIV.
In a joint statement, three of the world’s leading health campaign groups – the US President’s Emergency Plan for Aids Relief (Pepfar), UNAids and the Global Fund – said they were deeply concerned about the “harmful impact” of the legislation.
“Uganda’s progress on its HIV response is now in grave jeopardy,” the statement said.
“The stigma and discrimination associated with the passage of the Act has already led to reduced access to prevention as well as treatment services,” it added.
The legislation has also been condemned by Ugandan campaign groups, which are expected to institute court action to annul the legislation on the grounds that it is discriminatory and it violates the rights of LGBTQ+ people.
A similar law was struck down by Uganda’s constitutional court in 2014.
Ugandan rights activist Clare Byarugaba said it was “a very dark and sad day” for the LGBTQ+ community, and all Ugandans, Reuters news agency reported.
“The Ugandan president has today legalised state-sponsored homophobia and transphobia,” the activist added.
Parliamentary speaker Anita Among welcomed Mr Museveni’s decision to sign the bill into law, saying it will “protect the sanctity of the family”.
“We have stood strong to defend the culture, values and aspirations of our people,” she added in a statement posted to Twitter.
The bill was passed in parliament earlier this month, with only one MP opposing it.
The US has previously warned Uganda of possible economic “repercussions” if the legislation came into force.
The US is a major trading partner of Uganda. The East African nation benefits from the African Growth and Opportunity Act, which gives it easier access to lucrative US markets.
The US, UNAids and The Global Fund have also played a major role in backing Uganda’s long-standing efforts to curb HIV/Aids.
By 2021, 89% of people living with HIV in Uganda knew their status, more than 92% of them were receiving antiretroviral therapy, and 95% of those on treatment were virally suppressed, they said in their statement.
“Together as one, we call for the Act to be reconsidered so that Uganda may continue on its path to ensure equitable access to health services and end Aids as a public health threat by 2030,” the statement said.