Appearing in character as the Kazakh journalist, he referred to photos taken in 2016 when the couple were on holiday in Italy.
They featured Bloom paddleboarding while completely naked, accompanied by Perry in swimwear.
In the video message, Borat said: “Jagshemash Katy Pepsi!
View this post on Instagram@katyperry your dream come true birthday message my love HAPPY BIRTHDAY ❤️??@boratsagdiyev ?
“I was planning on going sailing in Florida and so I make an internet search for Orlando water sports but instead Mr Google sent me a photograph of your husband with his khrum out.
“He have a very good one. It must be nice to see Orlando Bloom. You have a very nice birthday. A lot of cream on your cake, why not?”
The video was shared by Bloom as a surprise for Perry’s 36th birthday.
Cohen’s wife Isla Fisher wrote in the comments: “And @katyperry you made my birthday dreams come true.”
While Borat referred to Bloom as Perry’s husband, the couple have not announced they are married.
He wrote: “@katyperry your dream come true birthday message my love HAPPY BIRTHDAY @boratsagdiyev.”
Bloom also shared a gallery of photos of the couple together, and wrote: “Happy Birthday my love. Oh the places we’ll go…”
Perry also re-posted the surprise video, writing simply: “Omg @orlandobloom.”
The Smile singer and the Pirates Of The Caribbean actor welcomed their first child, daughter Daisy Dove, in August.