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.

With more than 40 firms now offering gas and electricity deals it warns of the danger of one becoming insolvent.
At present anyone who is in credit with their energy supplier could lose out.
The watchdog wants the cost of a safety net to be paid for by customers, which would have "a small impact on bills", it said.
Ofgem's senior partner for consumers and competition, Rachel Fletcher, said: ""We are proposing a safety net to protect customers' credit balances in the unlikely event of a supplier failure."
Under current rules, if a gas or electricity supplier becomes insolvent Ofgem appoints a replacement to ensure that customers continue to be supplied with energy.
But it warns that "there may be financial implications for the failed supplier's customers".
That is because as direct debit energy payments spread the cost evenly across the year, customers are often in debit during the winter and build up credit in the summer.
Ofgem reckons that a typical customer's credit balance peaks at a little over Â£100 each year.
But it warns that without regulatory intervention, customers are unlikely to receive all - or possibly any - of their money back if their supplier fails.
Some industries already have a financial safety net for consumers.
If a financial services firm goes bust, for instance, the Financial Services Compensation Scheme protects people's savings with authorised firms up to Â£75,000. The scheme is paid for by a levy on all financial services companies.
Meanwhile if a travel company collapses, customers are protected if it was a member of travel trade association ABTA.  The scheme is funded through a bond on members.
Ofgem wants similar protection for energy customers and is proposing to allow, on a case-by-case basis, the costs of reimbursing credit balances to be spread across all energy customers.
"This would better protect customers' money and have a small impact on bills," it said.
The watchdog was keen to stress that it does not expect any suppliers to go out of business. "These proposals are for reassurance and to give customers the confidence to shop around and get the best energy deal," Ms Fletcher said.
But it points out that while competition benefits consumers, it can lead to suppliers to fail in the same way as companies can in other markets.
More than one in six - 17.4% - dual-fuel households are now with an independent provider, according to research from Cornwall Energy.
It says 7.1 million customers have switched to one of the energy market's newest players since 2011.
Hundreds of people have given their backing to plans for same-sex couples to be legally recognised in Guernsey.
[NEXT_CONCEPT]
The energy watchdog Ofgem has proposed adding a small levy to bills to ensure that consumers do not lose out if their supplier goes bust.