The man who skippered the Braves to unprecedented heights, and became so popular and so ingrained in Georgia summers that folks identified him by his first name alone, is officially bound for Cooperstown.

Retired manager Bobby Cox was elected to the National Baseball Hall of Fame by the Veterans Committee on Monday, along with Tony La Russa and Joe Torre. All three were unanimous selections by the 16-member committee.

Cox will be inducted July 27 at Cooperstown, N.Y., in a ceremony expected to have a distinct Braves flavor as pitchers Greg Maddux and Tom Glavine will likely be enshrined with their former manager.

“They say your life changes when you get elected to the Hall of Fame, and it has,” Cox said after the announcement Monday on the opening day of baseball’s Winter Meetings. “I’ve got goosebumps. It’s the greatest honor we could ever have. Hopefully two guys who helped get me to the Hall of Fame, Tom Glavine and Greg Maddux, will be inducted as well.”

Cox, La Russa and Torre are among the top five on the all-time major league wins list. Cox is fourth with 2,504 wins including a franchise-record 2,149 with the Braves, whom he managed to a record 14 consecutive division titles through 2005. His Braves won five National League championships and the 1995 World Series.

“The 16 years I spent with him were the greatest years of my life, and the only reason was Bobby Cox,” said Leo Mazzone, his longtime Braves pitching coach. “It’s only fitting that he goes in with those guys. It’s the most perfect scenario you could possibly imagine, except that Smoltzy has to wait another year to go in.”

John Smoltz, the other of the Braves’ vaunted Big Three starters, retired a year after Maddux and Glavine. There’s a five-year waiting period for Hall of Fame eligibility, but it’s reduced to six months for those who retire at 65 or older.

Cox, 72, retired after the 2010 season, his 29th as a manager including 25 in two stints with the Braves. Candidates from baseball’s Expansion Era are considered by the Veterans Committee every three years.

“(Cox) was a ferocious competitor, in the highest-class way,” said La Russa, who is third with 2,728 wins. “He would try everything to beat you.”

Torre was a nine-time All-Star as a catcher and corner infielder, including two All-Star seasons in three years with the Braves. He hit .315 with a career-high 36 homers in 1966, the Braves’ first year in Atlanta. As a manager, he ranks fifth in career wins and won four World Series titles in a five-year span with the Yankees.

Torre also managed the Braves for three years including an 89-win season and division title in 1982, after replacing Cox following his first managerial stint in Atlanta.

“Bobby and Tony were two different guys,” Torre said, “but the one thing, the one common thread, was how badly they wanted to win, and how ferociously they would compete.”

Maddux and Glavine, who each won more than 300 games and multiple Cy Young Awards, were Braves teammates for a decade through 2002, and are considered locks for election in their first year of Hall of Fame eligibility on the writers’ ballot. Those results will be announced Jan. 8.

“That’s really the way it should be, those guys going in together,” said retired third baseman Chipper Jones, who played his entire 19-year career in Atlanta, the first 17 seasons with Cox as his manager. “Those three guys, along with Smoltzy, were not only the braintrust and catalyst for all those division championships and our World Series championship and National League pennants and all that, but our whole world revolved around the arms of those three guys. And Bobby’s probably a reason those three guys stayed together as long as they did, how we kept it going so long here in Atlanta, because people wanted to play for Bobby.”

Said Glavine: “That was a big part of it. He was a big part of the culture in the turnaround for the Braves. We were all mindful of not only the team we had and the success we had, but what we had in Bobby. Guys on other teams used to always say, ‘What’s it like paying for Bobby?’ ‘I would love to play for Bobby.’

“You take stock in how good you had it, you’re mindful of it and don’t want it to go away. It was just such a fun time and a good atmosphere for everybody. It’s hard to believe any player is going to play under any better circumstances or in a better atmosphere than what we had all those years under Bobby.”

Cox had just three basic rules – show up on time, wear your uniform correctly, and play hard. He let players police themselves for the most part, and Glavine said the approach worked.

“It was one of those things where it worked almost in reverse, because guys had so much respect for him,” Glavine said. “Veteran players knew you had some leeway that young players didn’t have, but very seldom would guys take advantage of it, because there would be that sense of guilt. Almost like you were trying to put one over on your dad. We all know that feeling when you were a kid and you did something and your dad said, ‘I’m disappointed.’ It was kind of the same way with Bobby.”

“Nobody wanted to rock that boat, and when you were in good standing with Bobby you wanted to stay in good standing.”

Between managerial stints with Toronto and his second with Atlanta, Cox served as Braves general manager from October 1985 through October 1990. In that role he oversaw the groundwork for Atlanta’s subsequent success by drafting future standouts including Jones, Steve Avery, Mark Wohlers, Ryan Klesko, and Kent Mercker, and trading for Smoltz and Charlie Leibrandt.

“What makes him a Hall of Famer is his whole body of work, his whole professional character, his love of the game, and his success in the game,” said Braves president John Schuerholz, who replaced Cox as GM in 1990 and held the position for 17 years in what he called an ideal working relationship with Cox.

“There’s been few managers who’ve been successful to this level, and I don’t know of any that were as successful and had that unbending, unyielding belief in how great the game is. He’s always defended the game and the honor of the people who played the game.”

Cox remains employed by the Braves as a special assistant to the general manager, doing special scouting assignments and advising in organizational matters. He also spends much of his time working on business projects including a sprawling sports complex under construction in Emerson.

“I do miss the competition,” he said. “I miss when the umpire says, ‘Play ball.’ I really, really miss that.”