The switch-hitter said that he would take about 20 dry swings from both sides of the plate on Wednesday, and he's cautiously optimistic that he will be able to rejoin the Yankees' active roster in May.
"It's great. I started the process," Teixeira said. "It's all going to depend on how I feel now. I started very light yesterday, and it'll just be slow moving and hopefully feels good every day. We'll see where I am in a week or so on the next road trip."
"All the news that we've gotten has been encouraging," manager Joe Girardi said. "The real test is going to come when he starts taking BP and gets into games where the intensity is cranked up and you can't really guard what you're doing. I am encouraged that we've gotten this far."
Teixeira said that if the dry swings present no setback, his next days will involve progressing to hitting off a tee, soft toss, indoor batting practice and then finally hitting on the field.
Teixeira is hoping to take batting practice this weekend at Rogers Centre in Toronto. He will travel with the club to Florida and then continue working out at the Yankees' Tampa, Fla., training complex when the big league club plays against the Rays starting next Monday.
For the moment, Teixeira said just being able to swing a bat without discomfort is a good step.
"It's awesome," Teixeira said. "I have a bat in my office at home, and every time I check my e-mail or get something in my office, I kind of pick it up and just twirl it around a little bit. I haven't had a bat in my hand in a long time. It's very tough. It's great to have a bat in your hand again."
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.