The terms of the agreement have not been disclosed but it is understood Mackay was seeking substantial compensation for his dismissal, which came in December after a difference of opinion with owner Vincent Tan over the direction of the club.
Tan has since criticised Mackay's efforts in preparing the side for the Premier League following their promotion from the Championship last season, but the Scot issued a conciliatory statement through lawyers on Friday in which he apologised "without reservation" to the Malaysian businessman.
Mackay's statement, released through Slater & Gordon Lawyers, read: "Today I have reached a settlement agreement dropping all claims I have made against Cardiff City Football Club.
"I did not want to be in litigation and believe that it is in the best interests of all parties to have a clean break and move on.
"I have enjoyed my time at Cardiff City and I am most grateful to the board of Cardiff City and Vincent Tan for giving me the opportunity.
"The club's owner Mr Vincent Tan invested heavily in the club and supported our decisions in our push for promotion to the Premier League. Without him this would not have been possible.
"My thanks to all those at the club and the fans who have supported me during my time in Wales. If I have caused any offence to anyone during this time, especially to Vincent Tan, then I apologise without reservation.
"I wish everyone associated with Cardiff City FC all the best for the future and thank them for their support. I will not be commenting further on this matter."
The club responded with a brief statement of their own, echoing Mackay's comments and seeking to draw a line under the row for good.
"Cardiff City Football Club can confirm that Malky Mackay has dropped all legal claims against the club, bringing a number of issues to an end and allowing both parties to move on," it read.
"The agreement represents a positive outcome for the Club. We now look forward and focus fully on planning for next season and the challenge of regaining Premier League status."
Mackay was replaced by Ole Gunnar Solskjaer as manager in January but the Norwegian was unable to save Cardiff from relegation back to the Championship.
Mackay's former head of recruitment Iain Moody has also reached an agreement with the Bluebirds.