Koch wrote on Instagram alongside a video of the reunion.
"I felt like a two-week-old who was actually working hard to hold up my own head", she said, describing her first few days back in gravity.
In the adorable video, her dog LBD, which stands for Little Brown Dog, is seen eagerly waiting for her. When the door is opened, the dog immediately rushes into the arms of Koch, who exclaims, "hi baby girl!"
The pooch happily starts barking, jumping around and licking Koch - who can't help but laugh at the reunion - on the face.
"After 328 days in space, the first six days back on Earth were full of just as much wonder and excitement", she said to CNN. "Peggy is a heroine of mine and has also been kind enough to mentor me through the years, so it is a reminder to give back and to mentor when I get back".
When not busy performing experiments, Koch explained that she "soaked up the unique atmosphere" of the floating space lab by taking pictures and spending time with her crewmates.
Being in space for long periods of time can affect the human body in many different ways. The study is important because NASA plans to return to the moon under the Artemis program and prepare for the human exploration of Mars.
The US record for longest space flight is 340 days set by Scott Kelly in 2015-2016.