The three men were indicted in October 2016 for plotting an attack for the day after the presidential election in the meat-packing town of Garden City, about 350km west of Wichita.
US Attorney Stephen McAllister told reporters that the jury's verdicts represent "a victory for the rule of law and national security."
Prosecutors have said that a fellow militia member, Dan Day, became alarmed by some of his colleagues' threats and agreed to wear a wire as a paid informant. The government's case featured months of profanity-laced recordings in which militia members discussed plans and referred to the Somalis as "cockroaches."
"That confidential source is also to be commended for doing the right thing and the courage he demonstrated," McAllister said.
Wright is captured in one recording saying he hoped an attack on the Somalis would "wake people up" and inspire others to take similar action against Muslims.
"We welcome the guilty verdicts in this disturbing case and hope that anyone considering turning bigoted views into violent actions will see what their fate will be when apprehended and prosecuted by law enforcement authorities," said Moussa Elbayoumy, chairman of the Kansas chapter of the Council on American-Islamic Relations.
The government argued that the men formed a splinter group of the militia Kansas Security Force that came to be known as "the Crusaders." The testimony and recordings indicate the men tried to recruit other members of the Kansas Security Force to join them.
According to prosecutors, Stein was recorded discussing the type of fuel and fertiliser bomb that Timothy McVeigh used in the 1995 Oklahoma City bombing, which killed 168 people. Stein was arrested when he delivered 135kg of fertilizer to undercover FBI agents to make explosives.
Lawyers for the defence said the FBI set up the men with a paid informant and all the talk about violence wasn't serious. They said the men had a right to free speech and association under the US Constitution.
Prosecutors argued that the plot was more than just words.
The men discussed obtaining vehicles and filling them with explosives and parking them at the four corners of the apartment complex to create an explosion that would bring down and level the entire complex, McAllister said. They downloaded recipes from the internet and they experimented with and tested those explosives.
- AP
