Anderson, acquired by the Tigers from the Atlanta Braves at the end of Spring Training, hit .242 in 74 games this season.
Primarily a center fielder, Anderson swiped 13 bases in 15 attempts for the Tigers. A left-handed batter, he also had four triples, four doubles and 16 RBIs.
"He's a speed, defense-type player," general manager Dayton Moore said. "Historically, he's been a solid on-base guy throughout the Minor Leagues and in limited Major League time."
In six Minor League seasons, Anderson had a batting average of .294 and an on-base percentage of .344, with 280 stolen bases in 349 attempts.
The Royals lost some speed and defense when center fielder Coco Crisp was lost for the season because of shoulder surgery. Mitch Maier and, more recently, Willie Bloomquist have filled the position.
Both Moore and Hillman stopped short of saying that Anderson would become the regular center fielder.
"I wouldn't say that. He'll have to compete with what we have," Moore said. "Trey will make the decision on how he wants to do it. He'll certainly be an option in center field."
Anderson has played all three outfield positions, but he can cover a lot of ground, and playing center field would fit.
"If he does, that'll certainly help Willie's legs out a little bit," Hillman said. "We plan on utilizing him. I don't know that it's going to be every day, but we'll use him."
Bloomquist, who filled in at shortstop until the acquisition of Yuniesky Betancourt, could revert to his role as an all-purpose player. Maier, who just returned from Triple-A Omaha a week ago, could be at risk when Kansas City opens a roster spot for Anderson.
But the Royals weren't sure when Anderson might arrive because his wife is expecting a child.
"When he gets here, obviously we'll have to make a move and get him in the mix," Hillman said. "He's got some wheels, a left-handed bat and plays all three outfield positions, and has some basestealing history."
In 135 Major League games for Houston, Atlanta and Detroit, Anderson batted .283 with three homers, 39 RBIs and 24 stolen bases. His on-base percentage is .327.
Anderson, 26, was a fourth-round Draft choice of the Astros in 2003 and was traded to the Braves in 2007 for pitcher Oscar Villarreal. Anderson was the Player of the Year for Triple-A Richmond in 2008 with a .314 average, 25 doubles and 42 stolen bases.
He was designated for assignment by the Tigers on July 24.
Anderson, with his speed, could be a possibility for the leadoff spot in the batting order, although Hillman downplayed that possibility.
"I would imagine that he's probably led off plenty in his career. With this progress that David [DeJesus] has made, I would doubt that I would unseat David from that leadoff spot."
Meantime, with the Friday afternoon's non-waiver Trade Deadline approaching quickly, Moore was asked if the Royals had anything else in the fire.
"I don't have anything to report," Moore said. "We're just kind of working through it."