The 39-year-old actor popped the question to Katherine, 29, on 13 January following a whirlwind romance. "The Terminator" star Arnold previously revealed that Chris had done the traditional thing by turning to him to ask for permission beforehand, and Chris told U.S. TV show "Extra" that he was more than a little apprehensive about the prospect.
"I think any person who appreciates a tradition and asks a father for his daughter's hand in marriage, it's inevitably going to be something that makes you a little nervous, but that's sort of the beauty of it, you know?" he explained.
"He's a wonderful guy," the 71-year-old gushed. "They both look really great together, they're both happy together, so I wish them both the best of luck."
Chris and Katherine were reportedly introduced by her mother, Arnold's ex-wife Maria Shriver. And the author was quick to share her congratulations on social media after news broke of the engagement.
"Congratulations to two loving kind caring thoughtful Spirtual (sic) people," Maria commented on the Instagram engagement announcement. "We are so happy for you you are blessed as is everyone who knows you... yes let's go."
It will be the second marriage for Chris, who finalised his divorce from actress Anna Faris last autumn. The former couple share a son Jack, aged six.
According to reports, he and Katherine are planning a fall/winter wedding for later this year.