Teixeira said Wednesday at Georgia Tech that Rodriguez "has my 100 percent support," the Atlanta Journal-Constitution reported. Teixeira and Rodriguez were teammates on the 2003 Texas Rangers, when A-Rod tested positive for testosterone and Primobolan while winning his first American League MVP Award.
"I know he's going through a rough time right now, and I think his apology said it all," Teixeira said. "He's disappointed in himself, he made a mistake and we're all going to move on ... I'm just going to open up my arms, give him a big hug, tell him I love him and we're going to get through this."
Teixeira, who appeared at his alma mater pledging $500,000 to endow an annual Yellow Jackets scholarship, said that he was not surprised by Rodriguez's admission.
"I've been around long enough to not really be shocked by anything," he said. "This is a sport that's had some troubles, there's no doubt. I'm not going to judge anybody.
"I've never touched steroids or any of those kinds of things -- it's something I feel very strongly about -- but at the same time I've made mistakes, I'm not perfect, no one's perfect."
According to the report, Teixeira joked that his parents "would probably kill me before the media would if anything like that came out about me." He also said that he favored releasing all 104 names that came back positive in Major League Baseball's 2003 survey testing, which originally had been intended to remain anonymous.
"I think Lance Berkman put it pretty straight up when he said, unless the other names come out, everybody's going to be suspicious of the entire baseball world," Teixeira said.
A rookie in 2003, Teixeira said that he had no idea Rodriguez was using steroids then.
"I was really worried about staying in the big leagues," Teixeira said. "I came in as a third baseman, learned how to play first base and the outfield my rookie year, so I had no idea what was going on. I'd get lost [driving] to the stadium some days. I never saw anything, no one talked about it.
"That was supposedly the post-steroid era, we were getting tested and I was definitely not going to be messing around with that stuff when I'm getting tested. So I think if it was happening, and obviously it was, people didn't talk about it."
The Journal-Constitution reported that Teixeira has donated to Georgia Tech every year since he was the Rangers' first-round selection in 2001, but the $500,000 pledge marked his largest offering yet. The 28-year-old first baseman signed an eight-year, $180 million contract with the Yankees this offseason.
"I've been very blessed to be in the position I am now," Teixeira said, adding with a laugh, "It's no coincidence that I signed a contract and Georgia Tech is getting a nice donation now."
Teixeira is due to report to George M. Steinbrenner Field in Tampa, Fla., on Feb. 18 along with the rest of the Yankees' position players.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.