Delegates to the party's annual conference have voted overwhelmingly for a change in the law to recognise same-sex partners.
The controversial move would mean a same-sex partner would be treated like a husband or wife over issues such as inheritance, pensions, immigration, and adoption and fostering.
Lib Dems are the first mainstream party in the UK to back "civil partnerships".
Delegates to the conference supported a motion calling for a civil register of partnerships in England and Wales, for those who cannot or do not want to marry.
'Horror stories'
Gay and lesbian couples over 16 - banned from marrying at present - as well as couples who for other reasons do not want to marry, would be eligible to be registered.
The conference heard a string of impassioned pleas to give gay and lesbian couples equal treatment to heterosexual couples.
Former mayoral candidate Susan Kramer, who proposed the motion, told delegates about a lesbian woman seriously injured in an accident.
Her estranged parents, not her long-term partner, made the decision on when to switch off her life-support machine, and her partner was excluded from her funeral, she said.
"I have heard so many times about the experiences of people who cannot be recognised as next of kin when their partner has an accident and the decision has to be made on whether to switch off life-support, or people who have no right to inherit tenancies or benefit from pensions when their partner dies," she said.
"It is a series of horror stories which, on an individual basis virtually everyone would say were wrong and should not happen."
Supporters of traditional family life should not oppose the change, she said: "If you believe that stability is important for society, then stable relationships should be recognised."
Ms Kramer went on: "Discrimination has no place in the Liberal Democrat agenda."
Children's welfare
Before the debate, party leader Charles Kennedy signalled his support by stating: "I am in favour of tolerance and equality before the law."
MP Dr Evan Harris said research showed children in same-sex relationships were as happy and had the same chance of being heterosexual as those in mixed-sex relationships.
Both types of children were equally well-adjusted and developed peer-group friendships, he said.
The motion showed Lib Dems were the only party prepared to make children's welfare and equality a priority, he said.
Bigamy warning
MEP Baroness Ludford said it was a "landmark motion" but some details would have to be fine-tuned in legislation.
Richard Coxon said Liberal Democrats were the only party to say discrimination was wrong.
He said he was allowed a joint reward card with his partner at Sainsbury's, but his partner would not be allowed to have a say over switching off his life-support machine in hospital.
Delegates Vanessa Dowell and Sue Vincent supported the general aims of the motion but opposed the motion itself, saying the drafting was unclear or it did not go far enough in offering couples the option of gay marriage.
The motion failed to make clear people would have only one relationship at a time and would "give a green light to bigamy", warned Ms Vincent.
But delegates voted for it by a large majority.