KANSAS CITY, Mo. | The Kansas City Royals knew they’d uncovered something special when they saw Sean Manaea pitch in the Cape Cod League last summer, uncorking a pinpoint fastball that baffled some of the best amateur players in the country.

They kept their eye on the Andrean graduate this past college season, too, when every other team was sending scouts out to Indiana State. And when a hip injury popped up that could have hurt Manaea’s stock, the Royals viewed it as an opportunity to make a splash in this month’s draft.

The Royals’ keen eye and perseverance paid off — paid off for Manaea, most of all — when they announced Friday that they had agreed to terms with the big left-handed pitcher.

The 34th overall pick agreed to a $3.55 million bonus, more than double the recommended slot value of $1.623 million, and more in line with the sixth overall draft pick.

“One of the things that really solidified our judgment in Sean is the way he persevered this spring through the ups and downs, and really to his credit, tried to pitch through his injury,” Royals general manager Dayton Moore said. “That really solidified our judgment in who he is.”

Manaea will have surgery Monday to repair a torn labrum in his hip. He’ll need three or four months of rehab but should be ready to pitch by spring training.

“Sean is a player who came into the draft being one of the top arms in baseball. I think there was recognition of that fact on everyone’s part,” said his adviser, Scott Boras. “He had a minor injury, we’re assured he’s going to be back at 100 percent real soon, so we’re looking forward to seeing him perform at the levels he’s shown in the past.

“If he does,” Boras added, “I think we’re all going to be very happy with his future.”

Manaea was accompanied by his parents and brother for an introductory news conference on Friday at Kauffman Stadium, where he was presented with his crisp white jersey and royal blue hat.

“I couldn’t ask for anything better than what’s happening right now,” he said.

The 6-foot-5, 215-pound Manaea has a fastball that pushes into the upper 90s and a developing change-up and slider that made a mockery of hitters in the Cape Cod League. He struck out 85 while walking just seven in 52 innings, and was widely considered the summer league’s top player.

He wasn’t quite as sharp this past season at Indiana State, going 5-4 with a 1.47 ERA for the Sycamores. But despite pitching through his hip injury, sustained during a start against Minnesota in March, he still was third nationally with 11.4 strikeouts per nine innings.

“I feel like I had high expectations for myself,” Manaea said, “and I feel like I didn’t achieve those, but for the most part I felt like i did pretty well. It was just rough going through this injury right before the draft and all that.”

Many believe the hip injury is what caused Manaea to slip from the first round all the way to the Royals at No. 34 overall, the first pick of the competitive balance portion of the draft.

It sure didn’t hurt him much when it came to compensation. Manaea’s bonus breaks the record for a supplemental first-round choice set by Detroit’s Nick Castellanos in 2010.

The Royals had a feeling the price to sign Manaea would be steep, so they drafted shortstop Hunter Dozier with the eighth overall pick, far ahead of where most scouts had him pegged. That allowed Kansas City to reach an agreement with Dozier for a $2.2 million bonus, nearly $1 million below slot, and use some of that savings to help sign their new left-hander.

“He was a strong consideration for us where we picked (at No. 8),” Moore said. “You want to draft the best player you obviously can, but you want to maximize all your picks.”

Manaea was modest when asked to provide a scouting report on himself, but he did sound a bit like an experienced big leaguer when he chose to answer in the third person.

“When he’s on, he’s on,” Manaea said with a smile, while Moore and just about everyone else stifled a laugh. “He throws pretty hard when he’s not injured, and still needs a lot of work on his off-speed pitches, his change-up and slider. But he has a good head on him.”