Cornerstore was a place known for delivering babies and its employees are primarily storks, along with a few other birds. The current CEO of Cornerstore, a stork named Hunter (Kelsey Grammer), discontinued the baby delivering business, seeing more profit by converting the company to a parcel delivery service. However the last infant from before baby delivery was discontinued, Tulip, could not be delivered and was taken in by the company as an orphan.
Tulip (Katie Crown), having just turned 18 years old, is working to promote new ideas for Cornerstore, but they always backfire. Meanwhile Junior (Andy Samberg), Cornerstore's top delivery stork, is about to be promoted to boss of Cornerstore while Hunter is about to be promoted as chairman of the board. Hunter demands that Junior fire Tulip from the company due to her antics causing Cornerstore to suffer losses. Junior cannot find the heart to fire Tulip due to her kindness and hard work, he lies to her that she is being transferred to the mail room and instructs her to never leave her new office space.
Meanwhile, a young boy named Nate Gardner (Anton Starkman) feels lonely because his parents, Henry (Ty Burrell) and Sarah (Jennifer Aniston), are too busy to spend time with him and yearns for a younger brother. When his parents scoff at the idea and he learns from an old brochure about Cornerstore and their former baby-making reputation, he writes a letter asking for a baby brother and sends it to Cornerstore. The letter makes its way to Tulip, bored of waiting, who reluctantly leaves the mail room to put the letter in a slot just outside the room despite Junior's attempt to stop her, dislocating his wing in the process. The slot leads to the shut down baby factory (as she was supposed to put it in a containment of letters directly across). To their surprise, a baby girl is created inside a metal container, whom they later name Diamond Destiny.
Knowing that Hunter will fire him for creating an unauthorized infant and not firing Tulip as ordered, Junior agrees to secretly help deliver Diamond Destiny. As Junior's wing is broken, they use Tulip's flying machine for transportation. However, they crash into a frozen tundra. After a brief argument, Junior takes Diamond Destiny in the hopes of getting back to Cornerstore but is ambushed by two wolf leaders named Alpha (Keegan-Michael Key) and Beta (Jordan Peele) and their pack and taken to their cave, where Tulip was also captured. The two manage to save Diamond Destiny, whom the wolves have fallen in love with, and escape.
Back at Cornerstore, a pigeon employee named Toady (Stephen Kramer Glickman) learns of Diamond Destiny's existence. He goes after Junior and Tulip to confirm Diamond Destiny's existence, and upon reporting back to Hunter, he promises Toady Junior's position as they scramble the coordinates Junior and Tulip have been following to mislead them to a different location. After another brief encounter with the wolves, Junior and Tulip run into Jasper (Danny Trejo), an old stork that was ultimately responsible for Tulip being orphaned and the shut down of baby delivery after he broke her address beacon. Jasper reveals that he has been attempting to fix the beacon that would show Tulip's home but he was missing a piece, which Tulip had on her. Junior reveals that he was supposed to fire Tulip, leaving her in tears. Now knowing where her family is, Jasper decides to take her to be reunited with them while Junior sadly continues to deliver Diamond Destiny by himself.
Junior is captured and tied up by Hunter and his cronies at the false location and they kidnap Diamond Destiny. Tulip comes to rescue Junior without having met her family and the two resend themselves back to Cornerstore. After fighting an army of penguins, Junior and Tulip are chased into the abandoned baby making room and start up the machine as a distraction. As thousands of babies are being made, Hunter angrily confronts Junior and Tulip with a large robotic machine, but Junior refuses to surrender Diamond Destiny with Hunter's re-offered promotion. With the infant's playfulness, Junior and Tulip are able to cause the machine along with Hunter to fall off the cliff elevating the collapsing Cornerstore. After Junior flies for a short distance, it is revealed that Junior's wing was just dislocated.
Junior rallies the storks, as well as the other birds, to help deliver the babies to the families who wanted them including the Gardners. Upon delivering Diamond Destiny, Junior sees a vision of Diamond's childhood and womanhood. At first, Nate is disappointed that he didn't receive a brother, but when he goes to feed Diamond Destiny, she flings the bottle across the street using her ninja skills, therefore changing Nate's mind.
The storks, former employees of Cornerstore, and the wolf pack reunite Tulip with her expanded family, and she and Junior continue their job of delivering babies as co-bosses of Stork Mountain. In the end, every family now knows that storks deliver babies once again.