The 36-year-old Teixeira has been on the disabled list since June 4 with a right knee articular cartilage tear, which required injections of cortisone and lubricant products.
"Very excited," Teixeira said. "We really didn't know what to expect. We were hoping for the best and so far, it's been best-case scenario. We're hoping that the knee doesn't act up."
Teixeira will play first base on Tuesday, serve as the RailRiders' DH on Wednesday, then play first base again Thursday.
"I have to make sure that it bounces back; it would do me no good here if I can only play every other day," Teixeira said. "Three days will give us a good opportunity to test it."
It has been a difficult season for Teixeira, just one year after he was selected as an American League All-Star. In 48 games, Teixeira has batted .180 with three home runs and 12 RBIs.
"There's no excuses. When you're on the field, you have to perform," Teixeira said. "I'm going to put all that behind me whenever I get back on the field with the Yankees, because hopefully the injuries are behind me and I can just go out there and play, be healthy and produce."
In Teixeira's absence, the Yankees are platooning Ike Davis and Rob Refsnyder at first base. Because Teixeira is attempting to avoid season-ending surgery by playing with torn cartilage, Girardi said he expects that Teixeira may need additional rest after rejoining the active roster.
"You're probably going to have to," Girardi said. "It's probably going to be a fact where I'm going to have to check with him every day."
Bryan Hoch has covered the Yankees for MLB.com since 2007. Follow him on Twitter @bryanhoch, on Facebook and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.