The two treaties - on literary and artistic work and on the rights of performers and producers - mark the first time the international community has agreed terms to protect copyright for digitally transmitted material.
The "cyperspace copyright" agreement, subject to the approval of national governments, was seen as the biggest advance in copyright law since the Berne Convention on publications, agreed last century.
For the first time, recording artists will be protected when their material is distributed digitally, Jukka Liedes, the Finnish chairman of the talks, said.
The protection is seen as necessary given that digital transmission allows for perfect copying. "Madonna will now have the possibility for the first time to make her works available on the Internet and have her rights respected in the digital environment," he said.
The recording industry believes the market for music on the Internet could be worth $2bn (pounds 1.25bn) a year. EMI of Britain expressed satisfaction at the outcome of three weeks of exhausting negotiations, under the sponsorship of the United Nations. "This is an excellent result," a spokesman said. "We have long wanted protection in the digital age. The treaties were crucial."
Other so-called "rights holders" - ranging from publishers to musicians to software writers - were also pleased, pointing out that a new market could now develop for "pay-as-you go" entertainment, delivered to the home by computer.
A third treaty, which had been drafted to cover databases, was dropped when it became clear no consensus could be reached.
Several negotiators said the proposals would have seen copyright protection extended to facts, and not just expression - marking a radical and undesirable shift in copyright law. Had the third treaty been passed, they argued, databases such as soccer league statistics and stock prices would have been included.
Negotiators also dropped a controversial draft section that would have made online Internet service providers responsible for copyright violations even when computer users merely "surfed" the Internet.
Surfing requires the transitory copying of information, even if the user does not, in the end, seek access to it.
Service providers such as America Online and Microsoft furiously lobbied the US government to seek the removal of the offending clause, worried that they could be exposed to multi-billion-dollar claims by publishers and artists.
"So far so good," said Peter Harter of the Information Technology Association of America, a trade association. "We've done a lot of good here for the Internet."
The talks had been forced to a conclusion by the setting of yesterday's deadline. The 800 delegates will now return home, as the long process of national ratification begins.
A senior Iranian cleric called for restrictions on Internet access. "It should be limited to research and scientific centres," Ayatollah Ahmad Jannati said in a sermon at Tehran University. "Beyond that, it is poison fed to people." Iran's 10,000-plus subscribers must already pledge not to access "un-Islamic" information.