Johnson has been given permission to speak to the Premier League club after the fee was agreed this morning.
Cardiff had earlier rebuked offers from the Blues because of the low amount and the payment structure. Now though Peter Ridsdale has accepted a deal that should see Johnson move to the Premier league.
Speaking to the BBC Peter Ridsdale confirmed the agreement with Birmingham.
"We've said what the price would be... that's what we've achieved.
"We've merely given him permission to talk, it's up to Birmingham and Roger to thrash out a deal."
City signed Johnson from Wycombe and the Chairboys will get a sell on fee.
"On the assumption he goes it will be good value for a player we invested £275,000 in," Ridsdale said.
"There is a sell-on clause of profitability to Wycombe Wanderers and they'll be getting what they're owed out of this deal.
"But obviously that still leaves substantial funds for us and we will wheel and deal in the transfer market as best we can.
"What we have to do is to make sure that whatever money comes in we reinvest it and make us stronger than we were last year.
"Every football supporter has got to accept that every single football club is a selling club.
"It's not whether you sell that's the problem, it's how you invest the funds when you sell.
"What we've done at this football club is to build a new stadium and build a team that's got stronger each year and we'll continue to try and do that."
Johnson only missed one game last season, the home win over Burnley. That was because he was injured by a Claude Davis elbow in the previous match.
It's a shame City can't hold onto their best players with a view to mounting a serious challenge next season. We are used to this though. Maybe we'll bring in or bring through another gem.