"We've made a tough decision and the timing of this decision will have no doubt surprised and even shocked a lot of people," Cricket Australia chief executive James Sutherland told a news conference in Bristol on Monday.
"It's not a decision we've taken lightly, but a baggy green cap is something that is important to all Australian cricketers, it's one of the great prizes in Australian sport.
"What we feel is that Australian cricket fans expect and know that through the great history and tradition with the baggy green cap there is a responsibly for performance.
Sutherland said results had simply not been good enough.
"Consistency of behaviour, accountability for performance and discipline, they are things we like to see in a team that is improving." he said.
"We have recognised issues and concerns about that in months gone by and in recent times we haven't seen the improvement there that we would like. The coach is not solely responsible for that, but ultimately we've made a decision we believe will make a difference in this area."
Arthur said he took full responsibility for the situation.
"The reality is when you take a job on as head coach, you are totally responsible for the outcomes," he told a news conference.
"The players are a young group, learning their ways. I am a man of principal who tries to get the team going in one direction as I firmly believe that a team with culture is a successful team.
"I do not feel let down by the players at all, at the end of the day you live and die by the sword. I gave this job 100 percent of my time over the last couple of years and the disappointing thing is that I thought we were nearly there to cracking it."
Australia captain Michael Clarke, who has asked to step down from his role as a team selector, said he was initially shocked by events but was now fully focused on getting results.
"We know what the standards and expectations off the field are as well in regard to behaviour and we have no excuses for not upholding those values," Clarke said.
"We've been very disappointed with our performances so far on this tour and we have to turn that around."
Arthur was informed over the weekend that he was being let go despite his contract running until March, 2015.
The South African - the first non-Australian to coach the national side - took over in 2011 following a review into the humiliating 3-1 Ashes defeat, the first home series loss to England in nearly a quarter of a century.
The 45-year-old had previously coached South Africa to their first Test series victory in Australia before resigning after falling out with Cricket South Africa officials.
Early results were encouraging but after the heavy defeat in India they failed to reach the knockout stages of this month's Champions Trophy, a competition they had won the last two times it was held.
It may be, however, that Arthur has paid the price as much for the off-field problems as the on-field calamities.
In what became known as "homework-gate", Shane Watson, James Pattinson, Mitchell Johnson and Usman Khawaja were dropped from the third Test in India for failing to provide their thoughts on how Australia could improve in an e-mail.
David Warner's Twitter attack on journalists did nothing to counter the impression that discipline was an issue in the squad and it was compounded when the opener hit England batsman Joe Root in a bar after a Champions Trophy defeat, for which he was stood down until the first Ashes Test.
Lehmann, known in cricket circles as "Boof" and already in England with the Australia A team, was a left-handed batsman who played 27 Tests and 117 one-day internationals before moving into coaching.
He has won titles in all three forms in the game with Queensland and the Brisbane Heat and has signed a two-year contract with Australia.
"It's a challenge for all of the playing group, the team is going to play a certain way, an aggressive brand of cricket that entertains people and fans but also gets the job done on and off the field," Lehmann said.
"I'm excited by the challenge and certainly looking forward to working with Michael and the rest of team, and looking forward them having some success on this tour."
Australia play a four-day tour match against Somerset on Wednesday and the first Ashes Test starts at Trent Bridge on July 10.