The former Yorkshire left-handed batsman, 43, currently coach of Australia A, takes charge immediately.
Cricket Australia said Arthur, in charge for two years, was dismissed due to "struggles on and off the field".
Australia Ashes Tour itinerary
1st Test, Trent Bridge
2nd Test, Lord's
3rd Test, Old Trafford
4th Test, Durham
5th Test, The Oval
Cricket Australia CEO James Sutherland said: "This has been a difficult decision to make but one that we feel is necessary."
South African Arthur, 45, faced criticism following poor performances and disciplinary issues within the camp. He coached Australia to 10 wins and six defeats in 19 Test matches.
Lehmann, played 27 Tests and 117 one-day internationals for Australia between 1996 and 2005.
The 43-year-old retired from playing for South Australia in 2007, and was appointed as coach of Queensland in May 2011. He also recently coached Kings XI Punjab in the Indian Premier League.
Lehmann said: "It's a challenge for all of the playing group. I'm excited by the challenge, looking forward to working with captain Michael Clarke and the team, and seeing them enjoy some success on this tour."
Cricket Australia said he was the "outstanding candidate to drive the cultural change required" to take the team to the "number one ranking in all formats of the game".
They added that the decision as "drastic", but necessary "with such a big series fast approaching".
Cricket Australia explain Arthur sacking
The first Test against England starts on 10 July at Trent Bridge but Australia face two four-day warm-up matches first, starting against Somerset on Wednesday.
Sutherland said: "The timing is far from ideal but we didn't feel we could sit back and hope matters would change without addressing issues critical to a high-performing team culture.
"Recent on-field results have been too inconsistent.
"Discipline, consistency of behaviour and accountability for performance are all key ingredients that need to improve. We see that the head coach is ultimately responsible for that."
Lehmann played for Yorkshire between 1997 to 2006, was part of the side that won the County Championship in 2001, and captained the county the following season.
Darren Lehmann profile
Hits winning runs for Australia in World Cup Final
Helps Yorkshire to their first County Championship since 1968 with 1,416 runs
Takes catch for Australia to retain the World Cup
: Ends playing career after spell with Rajasthan Royals in the IPL
Coaches Deccan Chargers to IPL title
Coaches Queensland to Sheffield Shield in first season in charge of the state
Appointed coach of Australia
Queensland won the Sheffield Shield as well as two domestic one-day trophies in Lehmann's two years coaching the state.
On Lehmann, Sutherland added: "No-one is underestimating the task at hand but we believe he is the right man for the job. It is up to the players to respond under his leadership and demonstrate their commitment to a successful Australian team."
Off-the-field issues during Arthur's tenure included four players - vice-captain Shane Watson, Mitchell Johnson, James Pattinson and Usman Khawaja - being dropped for the third Test of the tour to India for failing to submit presentations on team strategy.
Then, in May, opening batsman David Warner was fined £3,700 (AU $5,750) for posting abusive comments to journalists on his Twitter account.
He was later suspended until the first Ashes Test, and fined £7,000 (AU $11,500), for punching England's Joe Root in a bar following Australia's defeat to England in the Champions Trophy.
Meanwhile, on-the-field, Australia last week finished bottom of their group in the Champions Trophy.
Cricket Australia also announced that Clarke had stood down from his role as on the team's selection panel.
"Being a team selector was proving to be a significant drain on Michael's time and he sees this as distracting from his primary responsibilities as a player and as captain," added Sutherland.
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