The Royals also selected the contract of right-hander Andres Machado from Triple-A Omaha and moved left-hander Brian Flynn (groin strain) to the 60-day disabled list to create room on the 40-man roster.
The Royals also recalled outfielders Terrance Gore and Paulo Orlando, along with catcher Cam Gallagher and middle infielder Raul Mondesi. Right-hander Trevor Cahill was activated from the DL after recovering from right shoulder impingement.
Royals manager Ned Yost also confirmed that the team added coach Mitch Maier. He will take over first-base coaching duties for Rusty Kuntz, who is battling vision issues, for the rest of the season.
Flynn and Feliz, who had a 4.74 ERA in 20 appearances with the Royals, were basically victims to their injuries.
"We need healthy arms right now," Yost said. "We can't wait."
Gaviglio made 12 appearances for the Mariners this season, 11 of those starts, and posted a 4.62 ERA and a 1.38 WHIP.
"He'll work out of the 'pen," Yost said. "He throws strikes."
Cahill also will move to the bullpen as he builds his arm strength back up.
Machado, a non-drafted free-agent signing in 2010 out of Venezuela, started the season at Class A Advanced Wilmington and was promoted twice. At Omaha, Machado, 24, was 2-2 with a 3.63 ERA.
"Dayton [Moore] started telling me about him a month ago," Yost said. "Throws hard, 95-98 [mph]. Throws strikes. He'll give us some bullpen help."
When Machado got the call he was heading to the Majors, he called his mom and dad back in Carabobo, Venezuela.
"I called my mom and when she answered [and I told her], she just cried," Machado said.
Machado said he modeled his pitching style after countrymen Felix Hernandez and Freddy Garcia.
"Fish [Royals senior pitching adviser Bill Fischer] said I look like and pitch like Felix Hernandez," Machado said. "I told him that was my favorite player."
Yost said that Mondesi will serve as a backup up the middle as well as speed off the bench.
"[Whit Merrifield] will need a break sometime down the line," Yost said. "He had an off-day yesterday, but he's been going at it pretty hard."