The Gabon international underwent a medical on Monday and, upon confirmation of the transfer, expressed his hope that he can push them back into the Premier League at the first time of asking.
"I have come here to Cardiff to soon play in the Premier League," he told the club's official website.
"I spoke at length to the manager [Ole Gunnar Solskjaer], who was a great player in this country. He has certain ambitions and I share those ambitions. The main one is to go back up to the Premier League and I'm very excited about coming here.
"I'm confident that things can go very well for me here. This is a good team with a good manager and a good board that is doing great work. I can't wait to start."
Manga becomes Solskjaer's ninth signing of the transfer window and the Norwegian revealed that the club had long been monitoring the 26-year-old.
"We've been waiting for this signing - Bruno is someone we've watched for a long time now," he explained.
"We faced stiff competition for his signing but managed to get the deal done. We're delighted; I said we would only add more before the window shut if something spectacular came up for us. It did and Bruno will be a terrific addition to our squad.
"Bruno will bring pace, international experience, energy and enthusiasm. He is a centre-back who plays the ball forward, looks up and can put us on the counterattack. I'm delighted he's agreed to join us."