Four members of the House of Representatives voted against the bill.
A rainbow flag was unfurled in the chamber as MPs cheered, clapped and hugged.
"When this law is passed, we should declare we are no longer a nation of people who voted no, or people who voted yes - we are simply Australians one and all", he said.
Those who opposed the bill were Bob Katter, Keith Pitt, David Littleproud and Russell Broadbent.
"Fair, diverse, loving and filled for respect for everyone", said an effusive Prime Minister Malcolm Turnbull, as he introduced the bill for a final vote.
'To claim that there will not be a range of adverse consequences for the freedom of speech, religion and parental rights.is wrong, ' Mr Andrews said.
Opposition leader Bill Shorten quoted the Book of Ecclesiastes from the Bible, adding a line that does not appear in the Old Testament - that there is a time for marriage equality.
"It's time for more marriages, more commitment, more love, more respect".
The legislation will become law as soon as it is granted royal assent by the Governor-General.
The House of Representative in the Australian Parliament has just voted in favour of passing a law that would allow same-sex couples to marry.
Many same-sex marriage supporters have travelled to Canberra to witness the outcome in the lower house.
The Senate last week approved the bill and rejected all proposed amendments that would have increased legal protections for those who would discriminate against gay couples on religious grounds. Changes suggested by the Greens were also defeated.
It went through unchanged, despite a push from conservative politicians for additional exemptions - including for religious organisations, civil celebrants and Defence chaplains.
Any amendments would have delayed the passage of the bill until at least next week as the changes would have been sent back to the Senate.
Drafting such measures into the Australian bill would delay it, but several gay marriage opponents have told Parliament this week they would not stand in the way of marriage equality because the Australian public clearly supported it in a recent postal ballot.