Little Tiana was reportedly born on Tuesday, April 17 and is the Fast and Furious star's third daughter.
Johnson posted a heartfelt message on Instagram to caption a photo of him cradling the infant.
"Skin to skin. Our mana. Blessed and proud to bring another strong girl into this world," he said.
"To my third and youngest daughter, Tiana Gia - like I did when your two older sisters Simone Alexandra and Jasmine Lia were born, you have my word, I'll love, protect, guide and make you laugh for the rest of my life.
"Your crazy dad has many responsibilities and wears many hats in this big ol' world, but being your dad will always be the one I'm most proud to wear.
"Oh and one more thing; you're going to love rolling in daddy's pick up truck."
Johnson said Tiana "came into this world like a force of nature" and that Hashian "laboured and delivered like a true rockstar".
He also gave some advice for other expectant fathers.
"Word to the wise gentlemen, it's critical to be by your lady's head when she's delivering, being as supportive as you can - holding hands, holding legs, whatever you can do. But, if you really want to understand the single most powerful and primal moment life will ever offer - watch your child being born. It's a life changer and the respect and admiration you have for a woman, will forever be boundless."
Johnson is currently in New Zealand cinemas in Rampage.