The EEOC also alleged that Emmert International retaliated against Redmon for complaining about the harassment.
The consent decree settling the suit, entered by Judge Clark Waddoups, requires Emmert International to pay $180,000 to Redmon and Brainich, provide training to its staff on unlawful employment discrimination, and to review and revise its policies on workplace discrimination.
The decree also requires Emmert International to post notices explaining federal laws against workplace discrimination.
A company spokesman did not return telephone calls for comment on the settlement.
The alleged violations occurred in 2009, when Oregon-based Emmert was working on a project to move Odd Fellows Hall, a 19th century building.
"Egregious racial harassment and retaliation are against the law, and employers must know that this type of conduct cannot be tolerated," EEOC Phoenix Regional Attorney Mary Jo O'Neill said in a statement. "We are pleased with the resolution of this case, and we are hopeful that this agreement will help highlight the need to prevent discrimination in the workplace going forward."
Racial harassment and retaliation violate Title VII of the Civil Rights Act of 1964.
The agency filed suit in the U.S. District Court for the District of Utah after first attempting to reach a pre-litigation settlement through its conciliation process, federal officials say.
"Employees everywhere should know that they do not have to tolerate racial harassment and that employees cannot be punished for standing up to this kind of unlawful harassment," said Rayford O. Irvin, director of the EEOC Phoenix District.
The Phoenix District has jurisdiction over Arizona, Utah, Colorado, Wyoming and part of New Mexico.