He wants to approve the law before foreign media to assert “Uganda’s independence in the face of Western pressure”, a spokesman said.
US President Barack Obama has cautioned the bill would be a backward step.
Mr Museveni had previously agreed to put the bill on hold pending US scientific advice.
“The president is signing the anti-homosexuality bill today [Monday] at 11:00 [0800 GMT],” government spokesman Ofwono Opondo told Reuters news agency.
“He wants to sign it with the full witness of the international media to demonstrate Uganda’s independence in the face of Western pressure and provocation.”
Homosexual acts are already illegal in Uganda.
The new law punishes first-time offenders with 14 years in jail, and allows life imprisonment as the penalty for acts of “aggravated homosexuality”.
The law makes it a crime not to report gay people. It covers lesbians for the first time, and criminalises the promotion of homosexuality – even talking about it without condemning it.
The bill originally proposed the death penalty for some homosexual acts, but that was later removed amid international criticism.
A gay rights activist in Uganda told the BBC’s Newsday programme he was “very scared” about the new bill.
“Actually I didn’t even go to work today [Monday]. I’m locked up in the house.
“And I don’t know what’s going to happen now. I’m talking to all my activists on the phone. And it’s the same, they are all locked up in their houses. They can’t move out. They are watching their back to see what happens.”
‘Affront and danger’
Mr Museveni’s renewed determination to sign the bill is an apparent U-turn from a recent pledge to hold off, pending advice from the US.
In a statement, Mr Museveni had said: “I… encourage the US government to help us by working with our scientists to study whether, indeed, there are people who are born homosexual.
“When that is proved, we can review this legislation.”
The US – one of Uganda’s largest aid donors – has warned that enacting the bill would complicate relations.
President Obama described it as “more than an affront, and a danger to, Uganda’s gay community. It will be a step backwards for all Ugandans”.
He warned it could “complicate” Washington’s relations with Uganda.
The US provides a reported $400m (£240m) in annual aid to Uganda.
In South Africa, former archbishop Desmond Tutu said he was disheartened by President Museveni’s apparent change of stance.