The photo revealed the baby's name is Grayson Robert Guiney and he was born at 2:10AM on Monday, December 3, weighing eight pounds and three ounces. Grayson also measured 21 inches long.
"Today is the greatest day!!" the new dad wrote in the caption.
"Our son, Grayson Robert Guiney was born early 12/3/2018. [Jessica] and baby are healthy and beautiful! Mom is resting with him on her chest right now. We are so excited and thankful for what this new day brings for our family!"
Bob and Jessica first announced the pregnancy in June, and through coordinating Instagram posts, they simultaneously revealed they had a baby boy on the way. The couple had posted photos from their blue-themed gender reveal party.
"We are both so excited," Bob told Us Weekly at the time, when Jessica was 12 weeks into her pregnancy. "I feel so lucky."
Bob and Jessica got engaged in October 2015 and tied the knot in November 2016 in Punta Mita, Mexico. Their nuptials concluded with a romantic honeymoon in Jamaica.
After Trista got engaged to Ryan Sutter -- her now-husband -- on the ABC reality series, Bob went on to star on The Bachelor's fourth edition that same year.
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Bob decided to give his final rose to mortgage broker, Estella Gardinier, but he offered her a promise ring instead of an engagement ring. The couple split shortly after the season aired on ABC.
Prior to meeting Jessica, Bob was married to soap opera actress Rebecca Budig from 2004 to 2010. Rebecca filed for divorce in April 2010 and the paperwork was finalized three months later. Bob's first marriage was to Jennifer Lantz.