They broke into the big leagues in 1994: Gene Budig as president of the American League, prodigy shortstop Alex Rodriguez as baseball’s handsome face of innocence in a season that ended Aug. 11, the World Series killed by a labor dispute.

Nineteen years later, they chatted for 15 minutes in a Joseph P. Riley, Jr. Park tunnel leading from the Charleston RiverDogs clubhouse to the dugout.

As part owner of the RiverDogs in the South Carolina town Budig calls home, the former Kansas University chancellor has a less stressful baseball job now as part owner of the Yankees’ Class A affiliate. Two decades, 14 All-Star Games, three AL MVP awards, several unproductive Octobers wearing Yankee pinstripes, multiple steroid scandals and one serious hip surgery later, Rodriguez no longer wears the face of innocence.

Yet, in many ways, A-Rod struck Budig on Tuesday — the first of two days the Yankee third baseman spent in Charleston on an injury-rehabilitation assignment — as the same friendly guy he remembered him being as a superstar shortstop with the Seattle Mariners.

“I always thought he was mild-mannered, very cordial, never forgot your name,” Budig said by phone from Charleston. “Very personable. Smooth. When he walked in, he instantly knew who you were and was ready to have a meaningful conversation.”

Rodriguez went hitless in Charleston, but was a hit nonetheless, according to his old friend.

“A-Rod made a lot of friends here,” Budig said, noting he signed autographs for at least 30 minutes. “Believe me, he could not have been more responsive to the fans. It was fun. He had a great time and was quite taken by the beauty of Charleston.”

From 1994 through 1999, baseballs Rodriguez signed already had Budig’s autograph embossed on them. Budig was the last AL president, a position that no longer exists.

“We joked about how many Budig baseballs he signed,” Budig said.

The Yankees’ plan calls for him to play 18 more minor-league games at various levels before returning to the parent club.

“We would have been delighted to have him for all 20,” Budig said.

Rodriguez is a drain on the parent club’s budget — he has five years and $114 million remaining on his contract — but he was great for business for the RiverDogs. “The Joe,” as fans call Riley Park, has a capacity of 6,000 and nearly 16,000, including many standing, watched Rodriguez play two nights, his first professional games since October.

“For a guy who hasn’t played in that long a period of time, I thought he moved well,” Budig said.

Resentment borne of October failure, his salary and steroid allegations — in that order — could greet Rodriguez upon his return to the Bronx.

“If anybody can deal with it, he can,” Budig said. “He’s played a lot of years. He’s been up. He’s been down. He’s seen good days and bad days and he somehow prevails.”