Renee Zellweger and Ant Anstead's relationship is "serious"

A source told PEOPLE: "There is so much respect between them.

"They spend as much time as possible together when they aren't working on other projects. They truly like each other as well as their romantic attraction. The relationship is serious."

The insider added that the 'Judy' actress and TV presenter have both found "stability" with each other.

They said: "Renee has found love again, a love where she feels confident and secure about herself. And Ant, too, has had a lot of ups and downs, but seems to have stability in this romance."

Another insider revealed that Renee has forged a close bond with Ant's son Hudson, two, who he shares with his ex Christina Haack, and that the pair "look very happy together" as they spend time together in California.

The source said: "Renee spends a lot of time with Ant in Laguna Beach. Ant is very focused on his son. Renee seems to very much understand this focus. She seems to enjoy all the fun outings with his son. She is always very playful and sweet with Hudson."

Ant recently explained that he and Renee are taking their relationship "one day at a time" and want to keep their romance as private as possible.

The 42-year-old star said: "Renee and my relationship is something that's really private. It's something I'm not really willing to talk too much about. It's really early in our relationship and I don't want to put any pressure on that."