On Monday the master address books for the net are being updated to include records prepared in a new format known as IP version 6.
Widespread use of this format will end the shortage of addresses that sites can be given.
The net's current addressing scheme is expected to exhaust the pool of unallocated addresses by 2011.
Although people use words to navigate around the web, computers use numbers. A human may type news.bbc.co.uk into a browser bar but the PC trying to reach that site will use a numerical equivalent that it gets from the net's master address books.
At the moment the vast majority of numerical net addresses are written in a format specified by version 4 of the Internet Protocol (IPv4).
On 4 February the master or root servers for the net will have a small number of records added that are written in IP version 6 (IPv6) added to them.
This means for the first time that computers using IPv6, typically a PC and a server, can find each other without involving any IPv4 technology.
Paul Twomey, president of Icann which oversees the addressing system, told the BBC News website there was a need to start moving to IPv6.
"There's pressure for people to make the conversion to IPv6," he said. "We're pushing this as a major issue."
The reason for the urgency, he said, was because the unallocated addresses from the total of 4,294,967,296 possible with IPv4 was rapidly running out.
"We're down to 14% of the unallocated addresses out of the whole pool for version 4," he said.
Projections suggest that this unallocated pool will run out by 2011 at the latest.
"There's not a Y2K problem per se," said Mr Twomey, "but there's going to be a crush so we need to get people applying for them now."
Under IPv6 an effectively inexhaustible pool of addresses becomes available.
Jay Daley, technology director at Nominet which oversees .uk domains on the internet, said many large companies were already using IPv6 as it helped ease administration on large internal networks.
Cable TV suppliers such as Comcast and NTT were using it to pipe IPTV to set-top boxes in customer's homes, he said.
Take up of IPv6 should start to increase, he said, as only recently regional organisations that handed out blocks of net addresses had relaxed the rules about who could get them.
Soon, he said, Nominet would start offering IPv6 addresses alongside IPv4 to those that wanted them.
"People are going to have to do it as IPv4 addresses become much more difficult to get hold of," he said.
For a long while, he said, the effects on consumers would be minimal though eventually home routers may have to be upgraded or swapped so they can use the longer addresses.