Greenwald and Poitras flew into New York's John F. Kennedy International Airport on the same flight to receive a George Polk journalism award for their reports on how the U.S. government has secretly gathered information on millions of Americans, among other revelations.
Their reporting on the leaks, which began last June, has sparked international debate over the limits of government surveillance and prompted President Barack Obama to curb the spying powers of the National Security Agency earlier this year.
"I really didn't expect anything to happen, which is why we finally came," Greenwald said to reporters shortly after embracing his partner, David Miranda, who had earlier said he was nervous as he waited for Greenwald to pass through airport security.
Last August, British authorities detained Miranda, a Brazilian citizen who lives with Greenwald in Rio, and questioned him for nine hours under anti-terrorism legislation when he landed at London's Heathrow Airport carrying encrypted Snowden documents.
Advocates for a free press have decried Miranda's detention and the British government's efforts to prevent the Guardian newspaper, which published many of Greenwald's articles, from running further stories about the Snowden documents.
Greenwald said he believed the U.S. government "wouldn't be that incredibly stupid and self-destructive" to detain him and Poitras in a similar way. When asked if he had carried Snowden documents with him, Greenwald repeated the question incredulously and laughed, saying, "No, I didn't."
Russia granted Snowden temporary asylum last year after the U.S. Justice Department charged him with violating the Espionage Act. Attorney General Eric Holder has said he does not plan to prosecute Greenwald for receiving and reporting on the leaks.
Poitras, an American citizen who lives in Berlin, has said U.S. authorities have detained and questioned her dozens of times when re-entering the United States and seized and copied her cellphone, laptop and notebooks.
She has said the increased scrutiny began after the 2006 release of her film "My Country, My Country", an Academy Award-nominated documentary about the effect of the U.S. invasion of Iraq in 2003 on Iraqi civilians and American soldiers.
Greenwald and Poitras are receiving their award jointly with the Washington Post's Barton Gellman, who also received documents from Snowden, and the Guardian's Ewen MacAskill, both of whom have been in the United States while reporting on the leaks.