At the end of the video, Perry can be seen cradling her baby bump, and she later took to Instagram to confirm the news.
The 35-year-old singer said: "I'm late ... but you already knew that.
"There's a lot that will be happening this summer, not only will I be giving birth - literally - but also figuratively to something you guys have been waiting for."
The couple are "excited and happy" about their baby news.
She said: "So let's call it a double whammy, a two fore.
"I'm excited, we're excited and we're happy - and it's probably the longest secret I've ever had to keep.
"I knew I would tell you in the best way, which is through a piece of music because that's how I speak to you."
And she joked: "I had to reveal it at some point, because it was getting pretty obvious."
Perry later thanked fans for their kind messages following her happy announcement.
She tweeted: "love u guys so much. was a bit nervous about sharing something so personal like the song n the bump n I hv never gotten this much love n support, it's overwhelmingly lovely. thank u #NeverWornWhite #babycat".