A Senate committee investigating marriage equality has recommended the Federal Parliament pass legislation to allow same-sex couples to marry.

The committee found significant support for marriage equality in the community, with almost 60 per cent of the 46,000 submissions received in favour of change.

It recommended the definition of marriage be changed and that the Marriage Equality Amendment Bill be debated and passed into law.

The chairwoman of the committee, Labor Senator Trish Crossin, has recommended all MPs now be given a conscience vote on the issue.

Two Opposition senators, Simon Birmingham and Sue Boyce, have also backed the recommendation and called for all parties to be given a conscience vote.

Senator Crossin says society is changing and so should the Marriage Act.

"We found as a committee that it is simply not relevant anymore to specify that [marriage] is an institution just for men and women alone," she said.

"This is an institution now that this society has recognised can be for two men or two women, for a man and a woman, for people who are transgender."

Greens Senator Sarah Hanson-Young, who put the bill forward, says it is a momentous day.

"Historical day. [It's the] first time we have support across the whole Parliament for reform to the Marriage Act, to remove discrimination to allow marriage equality to happen and to urge the Parliament to pass the bill into law," she said.

The national convener of Australian Marriage Equality, Alex Greenwich, says the committee's findings reflect community sentiment.

"We also are really excited that there was coalition support today for Sarah Hanson-Young's bill," he said.

"So for the first time we have coordinated support for reform in our parliament and that gives it a new burst of momentum."