Chambers was released from his Villa contract last week and joins the Bluebirds as a free agent.
The defender has penned a three-year deal and told Cardiff's website: “I’m absolutely delighted, and I can’t wait to get started.
“I think after speaking to the Club, it felt like they were very ambitious in where they were heading. It seemed like a really good project to be a part of, and I didn’t really want to miss out. I’m at a stage in my career where I want to be ambitious and create memories for myself as well. It was a good time for us both to meet at this point.
"The stadium is quality and it’s a great club. I can’t want to play here at the stadium for the first time. The manager was key. We had some good conversations, we’re both very ambitious and want to push this club up.
"It’s a very good squad as it is. I just want to come in as a centre half; I like to get on the ball and play, be vocal on the pitch, so if I can do that it will bring the best out of me as well.”
Cardiff boss Erol Bulut added: "First of all, he is a great player. He spent a long time at Arsenal and played at Aston Villa, so he will add great experience in our defensive shape. He is also an ex-teammate of Aaron Ramsey, so they will know each other. It is a great addition for us, and I hope that in our defensive shape and our build-up he will have good qualities. He can also play two or three different positions. That is important for us.
“I think it’s a good start to the window. Last season, we saw our issues in a few positions. In the attacking part, we created chances, but we couldn’t finalise them and I hope with Chris Willock, he will have different skills to what we had last season.
"With Chambers, he will be very important to our defensive shape. In football, you have to defend and attack together, and I hope that we can do that even better than last season because our targets are different this year.”