Icann oversees the structure of the net
The US government is expected to relax control over how the internet is run when it signs an accord with net regulator Icann on Wednesday.
The "affirmation of commitments" will reportedly give Icann autonomy to run its own affairs for the first time.
Previous agreements gave the US close oversight of Icann - drawing criticism from other countries.
Earlier this year, the EU called on the US to relinquish its control and Icann to become "universally accountable".
"The US government is the only body to have had formal oversight of Icann's policies and activities since its inception in 1998," it said.
"The Commission believes that Icann should become universally accountable, not just to one government but to the global internet community.
"This is particularly relevant given that the next billion of internet users will mainly come from the developing world."
The current agreement between the Internet Corporation for Assigned Names and Numbers (Icann) and the US Commerce Department's National Telecommunications and Information Administration is due to expire on Thursday.
Icann is a not-for-profit private sector corporation - set up by the US government - which oversees critical parts of the internet, such as the top-level domain (TLD) name system. Top level domains include .com and .uk.
The body recently voted to relax the strict rules on TLDs, meaning companies could turn brands into web addresses, while individuals could use their names. Icann also agreed to introduce domain names written in Asian, Arabic or other scripts.
The regulator has not yet released details of the new agreement with the US.
However, a report - described as "accurate" by people familiar with Icann - in the Economist magazine says the new deal does not have a fixed term.
It identifies a number of groups, including representatives of foreign governments, which will conduct regular reviews of Icann's work.
The panels would specifically focus on competition among generic domain names, how domain-name registrants' data are handled, network security and transparency, and accountability and the public interest - the only panel on which the US will reportedly retain a permanent seat.
A formal announcement about the deal is expected on Wednesday.
However, it is unlikely that the new agreement will sever the links between the US government and Icann entirely.
Rod Beckstrom, president and chief of the organisation, said in a letter to Congress last week that it would seek to maintain a "long term, formal relationship with the United States Government".
The body also has a separate agreement with the US - to run the Internet Assigned Numbers Authority (IANA) - that expires in 2011.
The IANA oversees the net's addressing system.