Sullivan and Brady said in a statement issued through their lawyers that they had received written confirmation no proceedings would be taken against them.
The decision follows a two-year investigation by City of London Police and Her Majesty's Revenue and Customs.
"Whilst always confident of this outcome, the period of the investigation was understandably a stressful time and David and Karren are now happy to put the matter behind them and look forward to the future," the statement said.
Sullivan and Brady were arrested in April 2008 as part of a police probe into alleged corruption in English football. The club said at that time that the investigation centred on payments to two players and a football agent.
Birmingham City has won promotion to the Premier League for the coming season.
Tax prosecutors said in a statement they had decided not to take criminal proceedings against two Birmingham City employees who they did not name.
A City of London police spokeswoman said: "A 60-year-old man and a 40-year-old woman arrested on suspicion of conspiracy to defraud and false accounting in April 2008 have been released from bail."
Birmingham City Chairman David Gold said on the club's website that he was delighted about the news.
"They have never done anything wrong and this is the correct decision," he said. "I have been inundated with messages from the wider family of football who are relieved with this decision."
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