The right-hander went 4-0 with a 2.61 ERA in six starts with the Rainiers and is expected to be called up prior to the game at Kauffman Stadium.
Beavan will replace Erasmo Ramirez in the rotation after Ramirez went on the 15-day disabled list on July 1 with a strained right elbow.
Beavan will have the added advantage of joining a Mariners squad that belted out nine runs on 11 hits in a 9-4 win Monday night. The team also crushed five extra-base hits, including three home runs.
"I loved the way they turned around some fastballs. We've been talking about that," Mariners manager Eric Wedge said of his team's run outburst. "If you're going to be a good big league hitter, you've got to be able to turn around a fastball. I don't mean just pull it, I mean meeting it where you need to in the hitting zone and drive it. And we did that a lot. We had 11 hits, but 7-8 hard outs as well."
Scoring seven runs in the game off Royals starter Jonathan Sanchez, Seattle knocked him out after just 1 1/3 innings and forced Kansas City to use Everett Teaford, the team's original starter for Tuesday's contest.
On Tuesday, the Royals announced that left-hander Ryan Verdugo will start.
Mariners: Ryan leaves game with bruised left knee
Mariners shortstop Brendan Ryan left Monday night's game against the Royals in the second inning after bruising his left knee by fouling a pitch off his leg.
Ryan stayed in during the at-bat and singled off Sanchez, later scoring on a triple by Casper Wells. However, Ryan was replaced on defense in the bottom of the second by utility infielder Munenori Kawasaki.
"It's a pretty good bruise," said Wedge. "He fouled a ball off his foot in batting practice and then really nailed his knee there on that one. It wasn't going to do anything but get worse. If we'd tried to push him through tonight, he's probably not going to be available tomorrow or maybe even the next day. So he came in and got treatment the whole game."
Franklin Gutierrez increased his pregame workout to include hitting in the cage as well as playing catch on Monday, as he works to return from the concussion he suffered June 29 when he got hit in the head with a pickoff throw.
Royals: Cain feeling well after latest collision
After crashing into the wall to make a spectacular grab in the ninth inning of Sunday's game against the White Sox, outfielder Lorenzo Cain said he felt fine on Monday.
The catch was similar to one that landed Cain on the disabled list earlier this season and required months of rehab.
"Everything's good. It's been a while since I ran into the wall. Definitely didn't end up good for me the last time I ran into the wall. But I'm feeling great after that incident yesterday," said Cain.
Royals pitchers Kelvin Herrera and Luis Mendoza will attend a baseball camp for kids with physical or developmental disabilities on Tuesday. The event is put on by the Royals and the Recreation Council of Greater Kansas City at the YMCA Challenger Sports Complex.
The Mariners have held a lead in 23 of their 53 losses this season, leading the American League.