It was mutual admiration between Zack Greinke and Dodgers brass

More than a week before deciding where he would pitch next season, Zack Greinke visited Dodger Stadium.

In his three decades as a baseball executive, General Manager Ned Colletti had been in countless meetings with prospective players. But this one was unique.

Greinke was there without his agent.

“I can’t remember one that didn’t bring an agent or friends with them or representatives with them,” Colletti said. “To have somebody with enough confidence in themselves to stand on their own, it was impressive.”

What was scheduled to be an hourlong meeting stretched into three hours. When Greinke left the ballpark, Colletti, President Stan Kasten and Manager Don Mattingly were in agreement: The Dodgers had to sign him.

They did, giving him with a six-year, $147-million contract. And Tuesday afternoon, they held a news conference to introduce him as their right-handed complement to ace Clayton Kershaw.

Looking back at the meeting, Colletti said, “Instead of getting to know the agent or the dynamics around the player, we got to know the kid. He was stunning. It was probably the best free-agent meeting I’ve ever had in decades of doing this.”

Greinke’s demeanor enhanced his on-field credentials, which included an American League Cy Young Award in 2009 with the Kansas City Royals.

The Dodgers found Greinke to be highly analytical and completely unfiltered. He described in detail how he would approach their hitters. He acknowledged that he had no idea how to pitch to Carl Crawford. He told them he liked their most recent first-round draft choice, infielder Corey Seager. When asked about his well-chronicled history with anxiety and depression, he told them it had been under control for several years with the help of medication.

“He is a scientist as a pitcher,” Kasten said. “I think he might remember every pitch he’s ever thrown to anyone and in what sequence.”

Greinke was also impressed.

Examining the Dodgers’ roster and farm system, he thought the team could compete for a World Series title every year for as long as he was there. He imagined he and his wife would like living in L.A. He liked how Dodger Stadium was a pitcher’s park, which would let him use a wider range of pitches.

Greinke was particularly taken by Kasten, who simultaneously ran Atlanta’s baseball, basketball and hockey teams.

“I don’t want to make his head too big, but I thought Stan Kasten was like the smartest guy I’ve ever talked to,” Greinke said. “With him in charge, I thought they had a good chance to keep things going good.”

He also liked Mattingly.

“Some of the things he said I really liked because it sounded like he’s striving to be better and is still learning,” Greinke said. “I think it’s impressive when a manager, or anyone, admits that there’s more to do, even if he’s already really good that he’s still trying to be even better.”

The Dodgers had something else Greinke liked: money.

“That’s what it gets to at the end,” Greinke said.

Greinke said he was leaning toward signing with the Texas Rangers until late in the process. The Angels, for whom he pitched in the second half of last season, remained in contact but never made a serious effort to sign him.

The Dodgers improved their offer to Greinke by $7 million in the 24 hours leading up to the agreement. That pushed the total value of the contract to $147 million, the most ever for a right-handed pitcher. The average annual value of the deal increased to $24.5 million, the highest for any pitcher on a multiple-year contract.

And although the Dodgers refused to include the no-trade provision Greinke wanted, they compromised. Greinke could void the remainder of the contract after three years and become a free agent. If traded, he could opt out of the deal at the end of that season.

“What’s the worst that can happen?” Kasten said. “He wins three Cy Youngs and leaves us?”

Dodgers acquire Schumaker

The Dodgers have an agreement in place to acquire utility man Skip Schumaker from the St. Louis Cardinals, according to a person familiar with the situation who was unauthorized to discuss it. The trade is contingent upon Schumaker’s passing a physical.

Hitting coach Mark McGwire pushed for the Dodgers to acquire the 32-year-old Schumaker, with whom he worked in St. Louis. Schumaker has played eight seasons in the majors, all with the Cardinals. He has a career .288 average.

The left-handed-hitting Schumaker is a career .305 hitter against right-handers. He is expected to share time at second base with right-handed-hitting Mark Ellis. Schumaker can also play all outfield positions.

Schumaker is entering the second year of a two-year, $3-million deal. He will get $1.5 million in 2013.

dylan.hernandez@latimes.com