COOPERSTOWN, N.Y. — One Hall of Famer after another was introduced onto the stage, each more impressive than the next. Legendary pitchers, all-around superstars, record-breaking home run hitters and wizards in the field.

Greg Maddux followed by Ken Griffey Jr., then Hank Aaron and Ozzie Smith.

None of them, however, can ever say what Mariano Rivera can.

He’s a unanimous member of the National Baseball Hall of Fame, the first ever player to receive a vote from all 425 members of the Baseball Writers’ Association of America in his first year on the ballot.

“To the baseball writers, thank you for voting for me and making me a Hall of Famer,” he said Sunday during his 25-minute speech to close out the steamy and emotional afternoon at Clark Sports Center in front of an estimated announced crowd of 55,000. “Thank you for all your support.”

Classy as always, the 49-year-old Rivera thanked everyone who had a hand in this momentous accomplishment, from coaches and teammates to family members, friends and fans in his native Panama. He singled out his longtime Yankees teammates Derek Jeter, Jorge Posada, Andy Pettitte, Tino Martinez and Bernie Williams — who performed a guitar solo preceding Rivera’s speech — all of whom were in attendance, and late team owner George Steinbrenner for always doing everything possible to make the Yankees a contender.

He thanked the team’s fans for always pushing him to be his best and didn’t fault them for even booing him on occasion.

“It’s a privilege and honor to be part of one organization,” said Rivera, baseball’s all-time saves leader with 652. “I did it with dignity, honor and pride. I tried to carry the pinstripes the best I could. I think I did all right with that.

“All those New York fans, when I was at Yankee Stadium pitching, I felt like I was pitching with 55,000 people next to me throwing one pitch after another. You guys are the best. Without your support, I cannot do it.”

Across his unparalleled 19-year career spent entirely with the Yankees, Rivera reached 13 All-Star Games and holds the lowest ERA (2.21) in baseball history for someone having pitched at least 1,000 innings. He was the linchpin to the Yankees’ dynasty in the late 1990s and early 2000s, almost automatic in the ninth inning, where he put up a 0.70 ERA and saved 42 games in the playoffs. He led the AL in saves three times and notched 40 or more saves in nine different seasons, a record he shares with fellow Hall of Famer Trevor Hoffman.

Rivera recalled the many ups of his immortal time in the game — it began with him signing with the Yankees out of Panama for $2,000 in 1990, along with a glove and cleats — but also the downs. He remembered how frustrated he was not to be able to communicate with teammates and coaches because of the language barrier early in his minor league career and getting sent down with Jeter in 1995 after struggling as a starting pitcher.

“Can you believe that now?” Rivera said laughing. “We were almost literally crying in Bennigan’s in New Jersey. We couldn’t believe it. But that only made us stronger.”

The turning point to his career, Rivera believed, was discovering the cut fastball in 1997. He recalled one day the ball moving like it never had before during a catch with teammate Ramiro Mendoza. He had no idea where it was going. During a bullpen session with late pitching coach Mel Stottlemyre, they tried to cut down on all the movement. But it wasn’t working.

“I said, ‘Leave it like this. Whatever’s going to happen is going to happen,’ ” Rivera recalled. “I learned how to use that pitch. I use that pitch for 17 years and I use it well.

“The Lord gave me the best pitch in baseball — the cut fastball,” he added.

It got him all the way to this day in Cooperstown, as the only unanimous Hall of Famer ever. And, of course, it included him closing out the ceremony in style, as he closed out 652 different Yankees victory.

“I think,” he said, “I was built for that.”