The results of a consultation by the Policy Council showed 90% of the 1,337 people who took part agreed or strongly agreed with the proposals.
Equality charity Liberate said: "It showed how far Guernsey had come, welcoming people from all backgrounds."
A report to be discussed by the States in December recommends same-sex marriage should be introduced.
In June, it was announced same-sex couples would be allowed to adopt under new laws agreed by the States.
Martin Gavet, from Liberate, said: "We have been traditionally treated effectively as second class citizens, although we pay the same taxes - simply because of who we are or who we love.
"Thankfully, we are living in much more enlightened times in which we have witnessed the decriminalisation of homosexuality and now we are seeing many jurisdictions recognising that love knows no boundaries - with equal marriage being introduced in 22 jurisdictions across the world to date.
"These proposals are reflective of how far our society has come and that it is the will of the majority and no longer the minority".
He added that the charity did not expect all faith groups to want to immediately carry out same-sex weddings.
Previously plans for the term "marriage" to be scrapped and a "Union Civile" law introduced - which would have allowed people to enter into legally recognised civil unions and remove links to religion - were dropped.
The Policy Council, which is responsible for Guernsey's constitutional and external affairs, launched the consultation in a bid to "modernise the island's legislation".
In Jersey last month, a move to introduce same-sex marriage was approved by the island's government.
The draft legislation, which will be voted on separately, is due to come back to the States of Jersey by January 2017.
In England and Wales, same-sex marriage became legal in March 2014.
Hundreds of people have given their backing to plans for same-sex couples to be legally recognised in Guernsey.