"She's in New Orleans at the moment doing a drama, The Thing About Pam, which is amazing," Anstead shared "I went out there a couple weeks ago to spend some time with her and am heading back out there this weekend."
According to the TV personality, the pair of them are both fans of exploring the iconic city's rich culture and colorful stories.
"I am fascinated by history. I'm a bit of a nerd when it comes down to it, so Renee and I did one of those ghost tours," Anstead said. "Bear in mind I am from London, where there's very old history, but wow, pirates, voodoo, all of it."
"We wandered into this little jazz room, and it was really amazing," he continued. "She's a good traveler and she's been to that city before, so it's nice. Looking forward to getting back."
"I think, when a child hits two, they call it the Terrible Twos for a reason," he explained. "I'd like to think that you try and get a routine and the moment that you give in they win. And I've given in! So I've been joining Hudson in bed at 4 o'clock every morning."
"I try and steal a few extra hours of sleep but the truth is that I'm [usually] half awake making sure I don't roll over," added Anstead -- who is also the father to 18-year-old daughter Amelie and 15-year-old son Archie, from his previous marriage.
This past summer, Anstead opened up to ET about unexpectedly falling for Zellweger while shooting his show, Celebrity IOU: Joyride.
"Sometimes things come to you at the right time, and actually the right time is often the most unexpected," he shared. "There's absolutely no way it was something I expected, but there's something magical in that, right?"
Check out the video below to hear more about the adorable couple.