Amawi, a dual US-Jordanian citizen, and El-Hindi, a US citizen born in Jordan, were also convicted of distributing information on making or using suicide bomb vests and improvised explosive devices (IEDs).
Prosecutors had charged that the three Ohio residents had conducted firearms training and accessed instructions on building and using explosives.
The defendants had also conspired to recruit others to participate in "jihad training," solicited funds to pay for the training and proposed sites to train potential recruits in the use of firearms, explosives and hand-to-hand combat.
Amawi traveled to Jordan in August 2005 with laptop computers for insurgents who were preparing to cross into Iraq, the Justice Department said.
The accused also distributed a guide on how to make chemical explosive compounds and a video entitled "Martyrdom Operation Vest Preparation," the department said.
For his part, El-Hindi distributed a slide show demonstrating how to make and use IEDs against apparent US military vehicles and soldiers and the same suicide vest video, it said.
They face life in prison for conspiracy to kill or maim persons outside the United States, 20 years for distributing information on explosives and 15 years for conspiracy to provide material support to terrorists.
"Today's verdicts should send a strong message to individuals who would use this country as a platform to plot attacks against US military personnel in Iraq and elsewhere," said Patrick Rowan, acting assistant attorney general for national security. "This case also underscores the need for continued vigilance in identifying and dismantling extremist plots that develop in America's heartland," he said.