A switch-hitter, Paredes spent parts of the last three seasons with the Astros, batting .234 with three homers and 31 RBIs in a total of 118 games.
"We saw him in Houston last year. He's an athletic switch-hitter that plays multiple positions," Royals manager Ned Yost said. "He's got an option left."
Paredes has also played third base and second base in the Majors.
Originally signed by the Yankees, he was included in the deal on July 31, 2010, that sent Lance Berkman to New York. Over seven Minor League seasons, Paredes has played 601 games with a .289 average and 166 stolen bases.
The Royals are Paredes' third team of this offseason. He was claimed by the Marlins last Nov. 4 and then by the Orioles just last Saturday.
Cleto, 25, had a 1-2 record and a 3.55 ERA in 19 games for Triple-A Omaha last season.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.