It's not illegal in the US.
The Electronic Frontier Foundation (EFF) wrote an article about the legalities in 2010.
They quote from a leaked memo from the Congressional Research Service (CRS):
This report identifies some criminal statutes that may apply [to dissemination of classified documents], but notes that these have been used almost exclusively to prosecute individuals with access to classified information (and a corresponding obligation to protect it) who make it available to foreign agents, or to foreign agents who obtain classified information unlawfully while present in the United States. Leaks of classified information to the press have only rarely been punished as crimes, and we are aware of no case in which a publisher of information obtained through unauthorized disclosure by a government employee has been prosecuted for publishing it. There may be First Amendment implications that would make such a prosecution difficult, not to mention political ramifications based on concerns about government censorship.
However, if you work for a US military organization (i.e. as a subcontractor for the Air Force, and I believe directly with military as well) it is absolutely forbidden to use any information obtained from WikiLeaks in your work. In a lot of organizations, it's forbidden to even look at WikiLeaks on a home or work computer. This appears to come from an order that was reportedly issued in 2010:
The Pentagon has banned the U.S. military from viewing anything related to WikiLeaks, the website for whistleblowers which controversially released thousands of classified government documents detailing the war in Afghanistan.
Wired reported that Air Force lawyers warned not even the children of military personnel are allowed to read it:
[I]f a family member of an Air Force employee accesses WikiLeaks on a home computer, the family member may be subject to prosecution for espionage under U.S. Code Title 18 Section 793,
However, they may have backed away from that claim:
Update, 4:15 p.m.: That was fast. An Air Force spokesman tells Josh Gerstein of Politico that the legal guidance is now under review: “We were just trying to give guidance to military and civilian servicemembers and employees to control their young’uns.” That’s the service’s business?
The practice of banning personnel from reading leaked information was still in place in 2014:
The U.S. military is now telling personnel in the Marines, Navy, Army and Air Force not to visit Glenn Greenwald's new journalism outfit the Intercept, and in some cases is blocking them from the website altogether.
Cuomo's claim, however, is incorrect. There is nothing keeping ordinary citizens from having these documents provided that they themselves did not steal them. It should be noted, however, that it is illegal to publish content from these documents if obtained through illegal means. However, the things that you see in the news are publicly released by WikiLeaks and therefore unless placed under an injunction are kind of fair game.