"Dawson entered the world on a very important day in our family. January 31st is not only my mom's birthday, but also the day my parents met 44 years ago," Ashley captioned the pictures.
Ashley posted a photo of herself posing with Jared and Dawson as well as a picture of Dawson wearing a light blue hat wrapped in a red-and-black checkered blanket.
Ashley also added photos of herself in the hospital, seemingly holding her new baby for the first time after delivering him, and Jared smiling big next to his son in the hospital.
"We pretty much had the best labor and delivery experience you could ever ask for thanks to INOVA Fairfax hospital and the NOVA Group For Women," Ashley continued in her post.
"I feared it forever and it wasn't that bad! I will go in-depth on the story eventually."
Ashley went on to share of her new life as a mother, "Right now we're enjoying the sleepiest, calmest baby we've ever met. Dawson did not get his chill from his parents."
"He did get his feet from me, his chin from Jared, one of his names from a [Leo DiCaprio] character [Titanic's Jack Dawson], and another one of his names from, well, see Jared's IG caption. We love him so much and are feeling so blessed!!" Ashley concluded.
Jared uploaded a photo of himself hugging his child and captioned it, "Meet Dawson Dimitri Brady Haibon."
Jared, a Rhode Island native, and Ashley apparently slipped the name Brady in there in honor of NFL quarterback Tom Brady -- arguably Jared's favorite football player of all time -- who just announced his retirement after 22 seasons and seven Super Bowl wins, six of which were with the New England Patriots.
It also appears Ashley and Jared have decided on Dimitri for the spelling of their son's middle name. When they first announced Dawson's name on Amazon Live last month, an on-screen graphic spelled it Demitri.
Many members of Bachelor Nation commented on Ashley and Jared's posts to discuss how cute little Dawson is and how happy they are for the new parents.
"Congratulations and God bless you guys," former The Bachelor host Chris Harrison wrote.
Joe Amabile called the baby "beautiful," and Tenley Molzahn gushed, "Bawling!!! He's perfection! You guys did it!!!! The best days are ahead. Love you all & congratulations!"
Vanessa Grimaldi wrote, "Wowwww what a gorgeous bundle of joy!!!!! CONGRATULATIONS."
Jared announced earlier this week that both Ashley and Dawson are healthy and doing well.
Ashley and Jared were living apart before the baby's birth, with Ashley preparing to deliver in Virginia at her father's hospital and Jared working at the couple's coffee shop and lounge in Rhode Island, which opened in December.
After about seven months of trying to conceive and Jared undergoing sperm analysis, the couple revealed during an Amazon Live session in July 2021 that they were expecting their first child and the baby was due on February 10, 2022.
Jared wrote on Instagram at the time how he appreciated his pregnant wife so much and thought she looked beautiful even when she felt sick.
"Ashley has been a trouper and I love her so much. Last night, she threw up five times throughout the night. It's been a very sick month for her," Jared revealed.
"I feel terrible because there's not much I can do except the occasional runs to the store for chocolate cake or to 7/11 for Slurpees. I love her very much, she's a strong woman and I know Ashley is going to be an incredible mother."
The pair then announced in August 2021 that Ashley was pregnant with a baby boy and they already had a name picked out for him -- a name Ashley had been sold on for about 20 years.
Ashley and Jared got married on August 11, 2019 at United Congregational Church Newport, RI, followed by a reception at Rosecliff, an oceanfront Gilded Age mansion in the seaside city.
Ashley has said in the past she would be happy to have up to three children.
The couple met in 2015 on Season 2 of Bachelor in Paradise, and they engaged in an on-again, off-again confusing romance on the show that simmered into a friendship in which Ashley largely pined for Jared as he dated other women on Season 2 and Season 3 of BIP.
Jared admittedly realized his feelings for Ashley and wanted what he couldn't have when she sparked up a romance with Canadian firefighter Kevin Wendt on The Bachelor Winter Games.
Jared eventually won Ashley over and the couple confirmed they were dating in May 2018.