Osher and his make-up artist wife welcomed their first child together on August 23, announcing the news via social media.
"We are in love and drowning in gratitude, oxytocin and new baby smell," the Bachelor host captioned the post, revealing he's in "complete awe" of Audrey.
"What I witnessed her do, the power I saw her summon from within her to bring this boy into the world was utterly astonishing. I can’t think of any single thing a man does in his life that physically equates to what I saw Audrey do.
"As he came closer and closer, her body began to unleash an incredible energy that was absolutely not going to be held back. Yet Audrey was able to harness it, guide it, and use it to transcend the extraordinary pain she was feeling and channel it all towards an energy that brought this boy alive and well into the world."
Although Wolfie is Osher's first biological child, he's also the proud stepfather of Audrey's daughter, Georgia.
The loved up couple— who tied the knot in 2016 in an intimate ceremony — announced they were expecting their bundle of joy in February.
"Our lives are already so full of love and adventures and I’m blessed to have such an amazing daughter in Georgia. Looking forward to meeting this little one and expanding my heart even more," Audrey wrote at the time.