"I plan on seeing him as regularly as we can," Hillman said.
DiNardo was 10-5 with a 3.35 ERA in 29 games, including 23 starts for Omaha, and was named the top left-handed pitcher in the PCL. DiNardo, 29, has a 10-15 record and 4.93 ERA in 89 Major League games with Boston and Oakland.
Hillman also clarified the order of his rotation, which was uncertain until DiNardo was slipped into the Thursday slot, giving ace Zack Greinke an extra day of rest after a long, tough game against the Angels.
Greinke will start on Friday night in the series opener at Cleveland, followed on Saturday by Luke Hochevar and Kyle Davies on Sunday.
That means just one extra day of rest for Greinke, who threw a career-high 125 pitches in holding the Angels to one unearned run in eight innings last Saturday night. His American League-best ERA is at 2.22.
"He really didn't want any more time off than that," Hillman said. "He was adamant that his body didn't need more than one extra day."
Greinke has piled up 198 1/3 innings, third most in the AL, and the Royals will monitor his workload closely as the season winds down.
"He hasn't had, to this point, any type of arm complications. He's got a delivery that allows him to do it. It's clean." Hillman said. "You don't really hold your breath or cross your fingers, but you keep checking the numbers."
However, he said Greinke won't have any "ceiling" on how long he'll go against the Indians on Friday night.
Hillman said the status of starters Gil Meche and Brian Bannister, both skipping starts because of shoulder fatigue, is uncertain pending more medical evaluation.
To make room for DiNardo on the 40-man roster, pitcher Doug Waechter was moved from the 15-day to the 60-day disabled list.
Previously, the Royals brought up pitchers Victor Marte, Carlos Rosa and Dusty Hughes from Omaha. Hillman said the DiNardo and Gordon promotions signal the end of September callups. That means that Omaha first baseman Kila Ka'aihue (.252, 17 homers, 57 RBIs) will not get a look this year, as he did in 2008.