He was 49.
Goddard was a courageous and relentless campaigner for the rights of gays and lesbians which are currently not recognised by the Zimbabwe Constitution.
Goddard also sat on the board of the Zimbabwe Human Rights NGO Forum (ZHR), which announced his death.
The ZHR said it was "sad to announce the tragic death of our colleague, Keith Goddard".
Goddard was "a champion of human, lesbians, gay men, bisexual and transgender rights in Zimbabwe and on the world stage", it added.
He was admitted to Harare’s St Anne’s Hospital after a short illness on Friday but succumbed later that night.
On its website, GALZ says it was formed in 1990 "with a membership of around 70 largely white, middle-class people". Goddard joined two years later and was appointed as the programmes manager in 1996.
On the website forum, Naison Manyenga, a former member of the GALZ "junior club members" now living in exile, in the United Kingdom, paid tribute to the man he claimed to have opened up the World for him.
In 2006, he was appointed as the director, a position he held up to the time of his death.
Goddard oversaw the setting up of a counselling hotline to "explore ways of challenging homophobic laws" and started HIV/AIDS campaigns, GALZ says on its website.
The organisation’s activities would grab international headlines in 1995 when having failed to get its counselling advert published in the newspapers, and finding itself under attack by government, GALZ decided to enter the 1995 Zimbabwe International Book Fair which had as its theme that year ‘Human Rights and Justice’.
The government banned GALZ from participating, and President Robert Mugabe slammed gays and lesbians as "worse than pigs and dogs". But the publicity surrounding Mugabe’s attack on gays and lesbians threw GALZ into the limelight both locally and internationally.