During his first news conference in the Bronx, Cole showed off both impressive knowledge of baseball labor history and the sign he carried to the 2001 World Series to cheer on the Yankees.

Credit...Danielle Parhizkaran/USA Today Sports, via Reuters

There is no mound on the field at Yankee Stadium in December, but Gerrit Cole still performed masterfully in his first home appearance in pinstripes.

Wearing a No. 45 jersey and a crisp Yankees hat at his introductory news conference on Wednesday, Cole captivated an audience of team executives, coaches and even some cynical reporters used to hearing dull platitudes from the megastars who arrive in the Bronx.

Cole distinguished himself by referencing the sport’s labor champions from long before his time, thoughtfully considering questions about expectations of multiple titles, and, in a grand flourish, brandishing the sign he took to the World Series in 2001, when he was 11 and cheering on the Yankees.

For the Yankees, the news conference was confirmation of the ease and confidence that had drawn them to him. For Cole, it was the culmination of a childhood fantasy.

“I can remember as a little boy dreaming about being a Major League Baseball player, specifically a Yankee,” Cole said. “It’s the right time and the right place to take that step.”

Cole grew up in Southern California worshiping the Yankees, who picked him as a high schooler in the first round of the amateur draft in 2008. But Cole elected to attend U.C.L.A. and was drafted No. 1 over all by the Pittsburgh Pirates in 2011. In 2018 he again eluded the Yankees when he was traded to the Houston Astros.

This season with Houston, he went 20-5 with a 2.50 E.R.A., finished second in the American League Cy Young Award voting and set himself up for a mammoth payday in free agency. He was said to have been pursued by several deep-pocketed teams.

The Yankees would not miss him a third time. They secured Cole with a nine-year, $324 million contract — a record amount for a pitcher — and Wednesday was the time to show him off to the world and articulate exactly why they had committed all that money.

“We need to win some world championships,” Hal Steinbrenner, the Yankees’ principal owner, said, “and I believe we’re going to do that. Sooner rather than later.”

Steinbrenner was asked to clarify: Did he mean more than one?

“Plural,” he said.

Cole, 29, did not shy away from the pressure of those expectations, or from the role he now occupies in that endeavor, as the ace of a team that just completed its first decade without a World Series appearance since the 1910s.

“It doesn’t scare me,” he said when told of Steinbrenner’s comments. “It’s what I dreamed of. Who wouldn’t want to compete for a championship every year?”

Steinbrenner acknowledged that he had declined to offer such big paydays for free agents when he had the opportunity in the past. But Cole was too special to pass up, he said. Brian Cashman, the Yankees general manager, commended Steinbrenner for adding the ninth year of the deal early in negotiations, saying it had separated the Yankees from the Dodgers and the Angels.

Cole, in turn, praised the Yankees with the type of language any new signee might use, calling them “the best organization in the league.” But Cole brought a prop to back up his words: He reached below the lectern to produce the sign he had taken to a 2001 World Series game in Arizona. It read: “Yankees fan today tomorrow forever.”

The pinstripes on the sign had faded, and the letters yellowed, but Cole insisted it was the one from his youth, when he became a fan of the club through the influence of his father, who lived in New York for a time.

“I mean, it’s 18 years old,” Cole said.

But perhaps it was most surprising when Cole took the opportunity to mention Marvin Miller, the longtime head of the players’ union who led the fight for free agency in the 1970s, and Curt Flood, the player who challenged the reserve clause, another big step in allowing players a chance to test an open market.

“We’ve seen competitiveness blossom and free agency blossom, and he played a major role in that,” Cole said of Miller. “Curt Flood as well. Challenging the reserve clause was essential to the blossoming sport we have today.”

Cole explained later that he had learned about the two from John Buck, a teammate in Pittsburgh who would challenge rookies on bus rides in a baseball version of the Socratic method. Buck would demand that the younger players tell him who Miller and Flood were, and why they were so important. That rubbed off on Cole, and when he finally had the chance to taste the fruits of their work and sacrifice, he did not forget it.

“I hope that goes on in every bus in the major leagues,” Cole said, “because challenging the reserve clause was one of the first steppingstones to, ultimately, the system we have today, which I believe brings out the most genuine competitiveness that we have in baseball.”

Now that the Yankees have Cole, the balance of that competition tilts a bit more in their direction.