Historically ICANN had authority via two mechanisms. The first is that it was appointed as the Internet Assigned Numbers Authority by the Internet Architecture

Historically ICANN had authority via two mechanisms. The first is that it was appointed as the Internet Assigned Numbers Authority by the Internet Architecture Board (part of the IETF). At a hard minimum that gives it the authority the run the IETF IANA functions, and historically would have been what gave it authority to issue IP addresses and AS Numbers. In performing the IETF IANA functions it has zero regulatory role, it is just a registry. I believe it has slightly more say over policy in issuing AS and IP addresses to the regional internet registries. The other (no longer applicable) source of authority was the contract from the US Department of Commerce. This is no longer applicable, as the US government decided it did not need to be involved with this, especially because it got a lot of criticism for being involved, but the contract really offered the government no real control over ICANN. The place where ICANN has the most say is domain names. Here ICANN acts as a full blown policy maker, in addition to running the naming IANA functions (like creation of the root zone file). To the extent that ICANN "regulates 'the Tnternet'", it is restricted to its policy setting over the DNS. It is less easy to give any current source of authority for this without the commerce contract. But it really comes down to everybody accepting ICANN as the provider of the root zone file, and the fact that ICANN would reassign the TLD delegations to a different registry if a currently assigned registry does not want to follow its rules. ----- The regional internet registries nominally get their authority to issue DNS address ranges from a delegation from the IANA (in its numbering function). Like mentioned before, one can trace ICANN's authority to run the numbering portion of the IANA back to being designated as the IANA by the Internet Architecture Board (part of the IETF), but this could be a little misleading, as the "numbering community" now exists, and ICANN claims that it is that community that would be allowed to appoint a new organization to run the IANA numbering functions. (Also ICANN has created a stand alone nonprofit to actually run the IANA functions. This is a membership based non-profit with ICANN as the sole member, making it basically like a subsidiary without legally being one, because ICANN wanted to make it very clear that the operation of the IANA functions is separate from the policy making part of the organization once the Government contract was stopped.) ------ Now perhaps you want to know how the IETF has authority? Quite simply, they are an outgrowth of, and assumed the functions of the Network Working Group, a group a early ARPANET researchers. As the group that defines protocols like TCP, IP, HTTP, etc they derive their authority from just that, that they develop the standards that underlie the internet.