Prosecutors say Madhi Hashi, 25, from Somalia, and Swedes Ali Yasin Ahmed, 30, and Mohamed Yusuf, 32, were members of the Shebab militant group in Somalia from December 2008 to August 2012.
Shebab is blacklisted as a foreign terrorist organization in the United States and federal prosecutors have spearheaded efforts to try foreign terror cases in New York courts in recent years.
Shebab has claimed responsibility for some of the worst terror attacks in East Africa, including a massacre at a Kenyan university that killed 148 people.
The Swedes fought against US-funded African Union forces in Somalia, prosecutors said. Hashi was close to Omar Hammami, the US-born public face of Shebab who was killed by fellow fighters in 2013, they added.
Yusuf appeared in a Shebab video to encourage recruits to travel to Somalia and join the group, and threatened a cartoonist who depicted the Prophet Mohammed — considered blasphemous to many Muslims.
US officials said the men were arrested by local authorities in East Africa en route to Yemen in August 2012, then handed over to the FBI in November 2012 and flown to New York to be prosecuted.
Acting US attorney Kelly Currie said the defendants were “committed supporters” of the Islamist insurgent group, which holds large swathes of territory in the south and centre of Somalia.
Since 2007, the United States has carried out more than a dozen drone and covert operations targeting Shebab, according to the London-based Bureau of Investigative Journalism which tracks US covert operations.
In September US missiles killed Shebab leader Ahmed Abdi Godane.