Sidney Nsubunga Enoch admitted in court that he had bludgeoned Mr Kato to death with a hammer, but alleged he had been provoked by sexual advances from him.
The murder sparked outrage, with Western governments calling on Uganda to legalise homosexuality.
Most Ugandans believe homosexuality is un-Christian and un-African.
School teacher
Mr Kato was killed after a newspaper published the names and addresses of people they said were gay or lesbian under the headline “Hang them”.
David Kato took on the Rolling Stone which was publishing photos of men it identified as gay
He was a school teacher and gay rights activist who had led a campaign against a controversial bill which included the introduction of the death penalty for some homosexual acts.
After the murder, Uganda’s parliament adjourned without debating it.
US President Barack Obama condemned the bill and donors have urged Uganda’s government to ensure it never become law.
Last month, UK Prime Minister David Cameron said the UK would reduce aid to countries that refused to legalise homosexuality.
Ugandan President Yoweri Museveni adviser, John Nagenda, accused Mr Cameron of adopting a “bullying mentality” and of treating Ugandans like “children”.
Homosexuality is illegal in most African countries.