His wife, Rebecca, gave birth to their second child back home in Houston on Saturday at 11:04 p.m. CST. They have a 3-year-old son, adopted from Ukraine.
Bresnik said both mama and baby are doing very well.
"Very thankful for everyone there at Mission Control and everywhere else at NASA that's been so supportive and essentially so helpful the last couple days with everything that's been going on," he said.
Mission Control responded with "heartfelt congratulations."
"Thanks for recognizing the significant accomplishments on Earth that happened while you guys were working hard on your challenging mission in orbit," Mission Control said.
The 42-year-old Marine installed antennas and other equipment outside the International Space Station on Saturday while eagerly awaiting his daughter's birth. Mrs. Bresnik was due to deliver Friday, but the day came and went, as did most of the next. The astronaut received the news privately in orbit.
Mrs. Bresnik, an attorney who specializes in international law at Johnson Space Center, said before the flight that she was "a little disappointed" her husband would not be present for the birth, but understood.
"We don't choose the timing," she said in an interview that was broadcast by NASA following the birth announcement. "He's trained one year for this mission but really he's been here five, almost six years. I'm just really excited for him and excited for us."
She said their son is eager to be a big brother.
This is only the second time a NASA astronaut has become a new father while in orbit. In 2004, space station resident Mike Fincke welcomed the birth of his second child, also a girl.
The shuttle astronauts were awakened Sunday by the song "Butterfly Kisses." Mrs. Bresnik chose it for her husband. Among the lyrics: "There's two things I know for sure/She was sent here from heaven and she's daddy's little girl."
Sunday was mostly a day off for the seven shuttle fliers and five space station residents, giving Bresnik time to savor the baby experience. He will venture back out on another spacewalk Monday.
Atlantis will remain docked at the space station until Wednesday. The shuttle will return to Earth on Friday. Mrs. Bresnik will not be on hand for the touchdown.