Legal action was taken against Ms Gibson after a newspaper story was published in April 2005 about the Beckhams.
Gibson had been employed by the stars as a nanny between May 2003 and March 2005, but after she quit the job she was interviewed by the News of the World and she had given out confidential information about the Beckhams to the newspaper.
A story based on what Gibson had revealed was published entitled "Beckhams behind closed doors".
Gerrard Tyrrell, who is the Beckhams' lawyer, said Ms Gibson "now accepts that she should not have breached her duties of confidence to David and Victoria Beckham and their children by speaking to the News of the World".
And he is reported to have added: "Ms Gibson has also agreed to the withdrawal of her claim for constructive dismissal that she made against the claimants which was issued in the Employment Tribunal in August 2005."
