The right-hander, 30, pitched in 25 games for the Royals with a 3.38 ERA in 29 1/3 innings. He was dropped when pitcher Wade Davis came off paternity leave just before the All-Star break.
"He'll do fine," Royals manager Ned Yost said. "He did a good job for us, he'll do a good job for them."
Gutierrez was a closer for the Diamondbacks during the time that present Angels general manager Jerry Dipoto was a D-backs executive.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.