"Baby #5 ....oh heavenly day," Emily captioned the video, which captured Emily repeating "oh my God" and "oh my gosh" once she learned she had just given birth to a baby girl.
Emily and Tyler's new baby was born weighing six pounds and 11 ounces, and Tyler can be heard saying the newborn looks just like Gatlin.
"Oh my gosh, that's so funny," Emily says in the video.
The video ended with Emily holding her daughter and posing for a family photo with her happy husband.
"It's a girl! Welcome to our world!" Tyler wrote in his own Instagram post, along with a video and interlocking-hearts emoji.
In Tyler's three-minute video, he documented Emily's trip to the hospital in the middle of the night and told his wife that she looked "so beautiful" in her hospital gown. Tyler then shared the same footage Emily had posted in her video.
Emily and Tyler also share sons Jennings Tyler, 5, Gibson Kyle, 4, and Gatlin Avery, who turns 3 in November. In addition, Emily is mom to a 15-year-old daughter Ricki from a previous relationship.
Ricki's father is her late fiance Ricky Hendrick, a race car driver who tragically died in a plane crash in 2004 just before Emily discovered she was pregnant with her first child at age 18.
After rejecting both of his Final 2 bachelorettes on The Bachelor's eleventh edition, Brad fell head over heels for Emily on The Bachelor's fifteenth season when he got a second chance at finding the woman of his dreams on reality TV.