Mr Cameron acknowledged that people would be "concerned" at Coulson having worked for him both as leader of the opposition and Prime Minister, but stressed that there had been no complaints about his work at No10.
The Prime Minister said he had asked the former News of the World editor whether he knew about phone hacking before he was hired, and received assurances which have now turned out to be false.
Speaking in the Cabinet Room at 10 Downing Street, Mr Cameron said: "I take full responsibility for employing Andy Coulson.
"I did so on the basis of undertakings I was given by him about phone hacking and those turned out not to be the case.
"I always said that if they turned out to be wrong, I would make a full and frank apology and I do that today.
"I am extremely sorry that I employed him. It was the wrong decision and I am very clear about that."