Wurtzbach, 26, commended the runner-up on Instagram.
"To Ariadna, you are an amazing woman and we are now bonded together forever by a unique experience. In the last 3 weeks we were together, I saw how strong and beautiful you are inside and out.
"You represented your country with honour and I know how proud everyone must be of you. Fate has a plan for you, and I'm excited to see what's ahead," Wurtzbach wrote.
"Wow. Words can't describe how grateful I am for this. It was quite a journey getting here with 3 attempts at winning Miss Philippines. Now, I finally got the best Christmas gift ever - and not just for me, for my country. I'd like to say thank you to everyone who believed in my potential and those who supported me from the beginning. To everyone who voted for me, especially to my fellow countrymen, thank you.