The Dublin-based agency went to the High Court in a bid to prevent Cox from taking a similar position at the rival agency Starcom MediaVest Ireland.
Cox resigned from Carat in March. He said he did not believe the 12 months gardening leave stipulated in his contract should apply. Carat disagreed and wanted to hold him to it. It said that working for Starcom created a clear conflict of interest.
The case was due to start last week, but an out-of-court settlement was agreed at the eleventh hour. Cox starts at Starcom on 1 September in the role of managing director.