He launched an unfair dismissal claim, demanding US$3.6 million in compensation or reinstatement, saying he was forced to take legal action because Cricket Australia officials had failed to get in touch with him following his sacking.
However, a confidential settlement has now been agreed.
"Both Mickey and CA agree that it is unfortunate that the dispute was not settled prior to the issuing of legal proceedings," they said in Wednesday's statement.
"Both parties agree that a resolution now is in the interests of the Australian cricket team and cricket generally in Australia.
"Cricket Australia appreciates the efforts that Mickey applied to his coaching role, and wishes him the very best in his future career."
In a separate statement, Arthur added: "I am very happy with the financial settlement we have reached with Cricket Australia.
"It was a real pity I had to launch legal proceedings but I'm glad we came to a settlement without the need to proceed with potentially expensive and protracted litigation.
"For me this was never solely about the money, I just wanted to be treated fairly and with dignity and respect.
"I have significantly reduced my claim as it has been settled tonight and is not dragging on at any significant cost."
Arthur was the first non-Australian to coach the team when appointed in 2011 following their 3-1 home Ashes defeat.
Australia have suffered a run of poor results recently, including losing a test series 4-0 in India and failing to make the knockout stages of the Champions Trophy.
They have also been troubled off the pitch, with four players suspended in India for failing to provide their thoughts on how Australia could improve in an e-mail, and David Warner suspended for punching England's Joe Root in a bar.
Australia trail England 2-0 in the five-test Ashes series.
The second test starts at Old Trafford on Thursday.
(Reporting by Josh Reich in London; editing by Ken Ferris)
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