"We are a small and marginalised community and when our rights are discussed in parliament, it makes us extremely happy," Tashi said.
The law had never been used, but Finance Minister Namgay Tshering, who submitted the recommendation to repeal sections 213 and 214 of the penal code, said they had become "a stain" on the country's reputation.
Namgay Tshering said the sections had become redundant since Bhutan became a constitutional monarchy in 2008. "There is a high degree of acceptability of the LGBT community in our society," he said.
The minister added that he was optimistic that the code sections would be definitively scrapped when the upper house in the country of 750,000 people votes on Monday.
Tashi said some ministers had been social workers with contacts in the LGBT community and Prime Minister Lotay Tshering is a surgeon. "So we had lot of hopes in this government."
There is no annual Gay Pride rally or other public display in Bhutan.
LGBT Bhutan said a lot more work needed to be done to change social attitudes and spread awareness of the challenges faced by members of their community.
"We have a big number of people supporting the LGBT people but still, a lot more is to be done /talked about," the group posted in a message on Facebook.
Tashi said although there was a general acceptance of transgenders, especially in rural areas, they still face much discrimination, especially in schools.
"There are lots of barriers and our education system does not understand LGBT," Tashi said, adding that most LGBT youths drop out of school.
Once the bill is passed by the National Council, the upper chamber, it will be sent for royal assent.