Cheers from the gallery greeted the key vote in the House, which passed it 198-176. Surrounded by gay marriage supporters, Lynch signed the bill about an hour later.
"Today, we are standing up for the liberties of same-sex couples by making clear that they will receive the same rights, responsibilities -- and respect -- under New Hampshire law," Lynch said.
Lynch, a Democrat, had promised a veto if the law didn't clearly spell out that churches and religious groups would not be forced to officiate at gay marriages or provide other services. Legislators made the changes.
Massachusetts, Connecticut, Maine, Vermont and Iowa already allow gay marriage, though opponents hope to overturn Maine's law with a public vote.
California briefly allowed gay marriage before a public vote banned it; a court ruling grandfathered in couples who were already married.
The New Hampshire law will take effect Jan. 1, exactly two years after the state began recognizing civil unions.
The Rt. Rev. V. Gene Robinson, elected in New Hampshire in 2003 as the first openly gay bishop in the Episcopal Church, was among those celebrating the new law.
"It's about being recognized as whole people and whole citizens," Robinson said.
"There are a lot of people standing here who when we grew up could not have imagined this," he said. "You can't imagine something that is simply impossible. It's happened, in our lifetimes."
Opponents, mainly Republicans, objected on grounds including the fragmented process.
"It is no surprise that the Legislature finally passed the last piece to the gay marriage bill today. After all, when you take 12 votes on five iterations of the same issue, you're bound to get it passed sooner or later," said Kevin Smith, executive director of gay marriage opponent Cornerstone Policy Research.
The revised bill added a sentence specifying that all religious organizations, associations or societies have exclusive control over their religious doctrines, policies, teachings and beliefs on marriage.
It also clarified that church-related organizations that serve charitable or educational purposes are exempt from having to provide insurance and other benefits to same-sex spouses of employees.
The House rejected the language Lynch suggested two weeks ago by two votes. Wednesday's vote was on a revised bill negotiated with the Senate.
Supporters had considered Wednesday their last chance to pass a bill this year.
The law will establish civil and religious marriage licenses and allow each party to the marriage to be identified as bride, groom or spouse. Same-sex couples already in civil unions will automatically be assumed to have a "civil marriage."
Churches will be able to decide whether to conduct religious marriages for same-sex couples. Civil marriages would be available to both heterosexual and same-sex couples.
New Hampshire's decision leaves Rhode Island as the only New England state not to allow same-sex marriages. A bill there is expected to fail this year, as similar ones have in previous years.
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