Gallegos was 0-1 with a 3.86 ERA and one save in 10 appearances at Triple-A, recording 26 strikeouts against six walks in 14 innings.
He split last season between Double-A Trenton and Triple-A, where he compiled a 1.27 ERA and 106 strikeouts in 78 innings over 44 appearances, leading all Minor League pitchers with a 12.23 K/9 IP ratio and a 36.1 percent strikeout rate.
"He's been pitching better at Triple-A," Yankees manager Joe Girardi said. "He's got a couple of different breaking balls, he's got a good fastball, he had a really good year in the Minor Leagues and he's been pitching better as I said."
Gallegos replaces right-hander Chad Green, who was optioned back to Triple-A on Wednesday after pitching a scoreless eighth inning in the Yanks' 5-3 loss to the Reds on Tuesday.
"For Green, we want him to continue to start," Girardi said. "Our bullpen is much more rested now after what we've been through, so everyone is available to me. We didn't feel like we needed a starter in a sense."
Gallegos, who was added to the Yanks' 40-man roster last November, said that his mother and sisters were making the trip from Mexico to New York in hopes of witnessing his big league debut.
"I'm so excited. This is a great organization," Gallegos said. "[I need to] just keep working. Welcome to 'The Show.'"
• Yankees first baseman Greg Bird (right ankle bruise) was scheduled to be seen on Thursday by team physician Christopher Ahmad. Bird was placed on the 10-day disabled list on May 2, at which time the Yanks said he would have seven to 10 days with no baseball activities.
• Girardi said that he read Derek Jeter's letter to fans that was published on Thursday via his Players Tribune Web site, and he is excited to see the Yankees' captain have his No. 2 retired by the team on Sunday.
"I think anytime Derek comes back, it's special, but this will be even more meaningful, I think," Girardi said. "And I think we've all been looking forward to it, I'm sure he's looking forward to it. I'm sure his family is really looking forward to it, and the one who seems to steal the show all the time is his nephew [Jalen], so I'm looking forward to that as well."