The 45-year-old Arthur, who was appointed as coach in November 2011, came in for sharp criticism following Australia's poor performances and disciplinary issues within the camp.
Cricket Australia chief executive James Sutherland said it was a difficult decision but it was taken to make Australia a better side.
"This has been a difficult decision to make but one that we feel is necessary. We are looking to establish a high performing Australian cricket team that is consistent over a period of time," Sutherland said.
"Discipline, consistency of behaviour and accountability for performance are all key ingredients that need to improve. And we see that the head coach is ultimately responsible for that," he added.
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Arthur, who had a contract till the end of the 2015 World Cup, said though it was disappointing he admitted that he could not do justice to his job.
"Naturally I'm very disappointed with how this has all ended. I certainly wanted to see the job through but I accept that the team hasn't been completely galvanised under my leadership and our performances have been inconsistent," said Arthur, under whom Australia has won 10 of 19 Tests, 18 of 39 ODIs and 7 of 16 T20s.
"Michael first approached Pat Howard in April after the recent Indian series and requested to stand down as a selector so that he could focus on his team's and his own preparation to play international cricket. This change will allow Michael to focus his primary responsibilities as a player and as captain," Sutherland said.