He made the comments prior to the Heat's game against the Denver Nuggets.
Wade disclosed in September on the Tonight Show with Jay Leno that he and Union had taken a brief hiatus from their long-term relationship, but had since reunited. On December 21, both Wade and Union announced their engagement on Twitter.
"In our time apart, in our break, in our pain and our hurt, a blessing came out of it in my life, having a son who was born healthy," Wade said.
Wade said the infant was approximately a month old.
"I got a chance to see him," Wade said. "I'm involved in my kids' lives, you know. When my kids lived at home with me, when they weren't living at home with me, I tried to do everything I could to see them."
Wade has two children, Zion and Zaire, from a previous marriage. In March 2012, Wade won sole custody of them after a contentious court battle. They were a focal point of his 201 memoir, "A Father First," in which responsible parenting was a central theme.
Asked if the event of the birth compromised the message of the book, Wade insisted it did not.
"It would compromise it if I wasn't a father first," Wade said. "This is something obviously private for my family that we will continue to deal with as a family. But we have a blessing, too, to the bloodline, the Wade bloodline. From that standpoint, to me, it doesn't state anything differently than what I've always shown."