Blues boss Alex McLeish sealed a season-long loan deal for Manchester City goalkeeper Joe Hart on Wednesday morning, and has wasted no time in moving back into the transfer market to bolster his back line - with Johnson rated in the £5million bracket.
"We can officially confirm that we have come to a financial agreement with Birmingham City Football Club for the permanent transfer of Roger Johnson," Cardiff said in a statement.
"Roger has now been given permission to talk to the newly promoted Premiership side."
Cardiff have been resigned to losing Johnson this summer after he expressed a desire to join a Premier League club.
Johnson, 26, has made 129 appearances and scored 14 goals for Birmingham since signing from Wycombe for £275,000 three seasons ago.
If the deal goes through, the 6ft 3in Johnson is likely to partner another new signing, 22-year-old Scott Dann, who has joined Birmingham from Coventry.