The reform gives gay men and lesbians full marital rights, and allows them to adopt children.

At present, same-sex couples are limited to civil unions.

Mrs Merkel's political opponents were strongly in favour. But Mrs Merkel, who only gave MPs the go-ahead on Monday, voted against.

She had told deputies in her conservative Christian Democrat party (CDU) to "follow their conscience".

Norbert Lammert, president of the parliament, said 393 lawmakers voted to approve the amendment, while 226 voted against and four abstained.

The German legal code will now read: "Marriage is entered into for life by two people of different or the same sex", AFP news agency reported.

How did Merkel prompt the vote?

During her 2013 election campaign, Angela Merkel argued against gay marriage on the grounds of "children's welfare," and admitted that she had a "hard time" with the issue.

But at an event hosted by the women's magazine "Brigitte" on 26 June, she shocked the German media by announcing on stage that she had noted other parties' support for it, and would allow a free vote in the future.

The usually-cautious chancellor said she had had a "life-changing experience" in her home constituency, where she had dinner with a lesbian couple who cared for eight foster children together.

As the news spread on Twitter, supporters rallied under the hashtag #EheFuerAlle (MarriageForAll) - and started calling for a vote as soon as possible.

Does gay marriage have popular support?

Yes - a recent survey by the government's anti-discrimination agency found that 83% of Germans are in favour of marriage equality.

The day after the Republic of Ireland voted to legalise gay marriage in May 2015, almost every German newspaper splashed a rainbow across its front page.

"It's time, Mrs Merkel" Green party leader Katrin Goering-Eckhart exclaimed then. "The Merkel faction cannot just sit out the debate on marriage for everyone."

Why is this happening now?

Because of an upcoming general election.

Germans go to the polls on 24 September, and the sudden Merkel turnaround will deprive her opponents of a campaign issue.

The Greens, the far-left Linke, and the pro-business Free Democrats all back same-sex marriage. In fact, they have refused to enter a future coalition deal unless reform is agreed on.

Mrs Merkel's current coalition partners - the centre-left Social Democrats (SPD) - have done the same.

The right-wing Alternative for Germany (AfD) is now the only party to oppose same-sex marriage.

Conservatives within Mrs Merkel's party, the Christian Democrats (CDU), are against a change in the law, however.

They have argued that a gay marriage bill would require a change to the constitution, and that marriage between a man and a woman should enjoy special protection.

The CDU's Bavarian sister party, the Christian Social Union (CSU), has also expressed opposition.

Its members champion "traditional" families - and pragmatist Mrs Merkel needs their votes in the September election.

Commentators say this partly explains why she has rejected a vote on marriage equality until now.

How did Merkel's opponents react?

Amid a groundswell of public support for a vote, Mrs Merkel's rivals have moved to capitalise politically.

A day after her comments, the SPD's candidate for the chancellorship Martin Schulz declared - "we will take her at her word," and called for an immediate vote.

The Greens and Linke promptly backed the prospect.

The CDU responded by condemning the SPD, its coalition partner, for its "breach of trust" after four years of joint rule.

The angry exchange came just days after Mr Schulz angered conservatives by accusing Mrs Merkel of an "attack on democracy", saying she was deliberately making politics boring so that opposition supporters wouldn't bother to vote.

Has the vote been politicised?

On Wednesday, Mrs Merkel branded the political dispute "totally unnecessary" in an interview with business weekly Wirtschafts Woche (in German)..

"This isn't about some legislative footnote, but... a decision that touches on people's deepest convictions and on marriage, a cornerstone of our society", she said.

Die Welt, a German national daily agreed.

"This could have been a great moment for Germany's parliament. But the CDU/CSU have been forced into a corner and all the joy has been drained," it wrote.

Where else in Europe has same-sex marriage?

A host of European countries have beaten Germany to a same-sex marriage law.

Civil marriages are legally recognised in Norway, Sweden, Denmark (excluding the Faroe Islands), Finland, Iceland, the Netherlands, Belgium, Spain, Portugal, Luxembourg, France, the UK (except Northern Ireland and Jersey), and the Republic of Ireland.

But in Austria and Italy - as in Germany - gay couples are restricted to civil partnerships.

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