Lucas will challenge Jack Butland and Colin Doyle for a starting spot at St Andrew's.
The 34-year-old ex-England Under-20 international has signed a one-year deal with the club after leaving his player/coach role at Spotland in May.
Lucas has also enjoyed spells with Leeds, Sheffield Wednesday, Swindon and Barnsley.
"I'm delighted to welcome David to the club and he will now compete with Jack and Colin for the number one spot," manager Lee Clark told the club's official website.
"It's very important for us to always have three senior goalkeepers to call upon because, for example, we could find ourselves without Jack Butland for the Capital One Cup tie against Barnet due to international duty."