Johnson, a Lockheed Martin employee who maintained helicopters, was kidnapped last Saturday from his Riyadh home and held captive by terrorists who demanded the Saudi government release al-Qaida prisoners and banish Westerners from the kingdom.
Powell said the United States condemns the execution.
"It's an action of barbarism, an action that shows once again what the world is dealing with -- these kind of individuals who would behead somebody or murder somebody in cold blood, an innocent individual who was just trying to help people and trying to do his job," Powell said.
"The murder of Paul shows the evil nature of the enemy we face. ... There's no justification whatsoever for his murder, and yet they killed him in cold blood," Bush said in a statement issued by the White House.
The Council on American-Islamic Relations, an Islamic civil rights and advocacy group in Washington denounced the "act of senseless violence and ... all those who believe such murderous behavior benefits the faith of Islam or the Muslim community."
Tom Jurkowsky, a spokesman for Lockheed Martin, the company that employed Johnson, said, "We're very distressed, very disheartened." Jurkowsksy told CNN the company is dealing with the family.
Johnson's family, who live in Ocean County, N.J., declined to comment. However, messages of condolences were flooding a Web site, www.nj.com/forums/ocean/.