The 28-year-old centre-back, who helped Birmingham to Carling Cup glory before being relegated from the Premier League last season, has agreed personal terms on a four-year deal and returned to Wolves' Compton training ground to sign his contract.
The defender becomes Mick McCarthy's third signing of the summer after the arrivals of Jamie O'Hara and Dorus De Vries, and Wolves insist he has been a target for several years.
"We tried to sign Roger two years ago when he moved from Cardiff to Birmingham and have been tracking him ever since," chief executive officer Jez Moxey told the club's official website.
"We are pleased to have signed what we believe to be an excellent player who represents good value for money for us.
"He fits the bill perfectly - a British centre-back in his prime, one with Premier League and cup-winning experience, a vocal, determined, leader type who has played consistently well for a long time.
"We stressed that we would not rush to do deals this summer and would have to be patient in the pursuit of our targets, which has proved to be beneficial for us."
Reports had suggested Wolves, having decided against Matt Mills, who has joined Leicester from Reading, will pay Birmingham a fee of £7million.
But Moxey is adamant this is an exaggeration, as he said: "As soon as Birmingham were relegated, we started negotiations and these went on for a long time but it got to a stage where we looked like we might not be able to sign him.
"At that point we started talking to Reading about Matt Mills. But it soon became apparent to us that Matt Mills was unlikely to represent the value for money player we wanted.
"There was also a lot of misinformation in the press about the money we were supposedly offering - we only made one formal bid and the figures quoted were exaggerated.
"Likewise, while we are sticking to our policy that all transfer fees agreed remain undisclosed, the reports concerning the deal with Birmingham are also inaccurate."