The couple are already parents to sons Noah, 8, and Elias, 6, and daughter Vida, 3.
Last month, Bublé told People the music video was a "very cool family affair."
It was the "most fun" he'd ever had making a video, he said, despite three "intense" days of filming on 11 different sets.
"I'll Never Not Love You" is the follow-up to the video for his 2009 hit song "Haven't Met You Yet," which also starred his wife.
Bublé said he'd found the idea of balancing his roles as both a dad and a full-time artist to be "non-existent".
"You know that one will always be hurt by the other," he said. "In my case, I will never allow my job to interfere with being a father and a husband — that's gotta be first, and everything else is a bonus.
"I think I have a lot of integrity in whatever I do work-wise, but that integrity is there because my family keeps me grounded," he added.
The couple's pregnancy news was first reported by TMZ.