The world's leading Test wicket-taker is already working with Australia's top spinner Nathan Lyon as part of Australia's National Cricket Centre Spin Programme, and has agreed to become more involved.
His signing is a coup given his knowledge of the doosra delivery, which has long baffled the Australians, and with Pakistan's Saeed Ajmal among the game's most potent mystery spinners.
"I know the Australian team is a very good side, but hopefully I can have a little bit of input to help them do well in the series against Pakistan," said Muralitharan.
"Ajmal is a difficult customer for all the best batsmen in the world, but he bowls a little bit similar to me so perhaps if I can bowl to the Australian batsman it might help a little bit and give them some tips."
The 42-year-old retired from international cricket after Sri Lanka lost the World Cup final to India in 2011.
Muralitharan's role will be similar to that filled by fellow spin legend Shane Warne on the recent tour of South Africa.
"Muthiah Muralitharan is a true great of the game and his involvement with the Australian team will bring enormous benefits," said Lehmann.
"He really understands the conditions we'll face and will be able to impart a great amount of knowledge. Not only will he help guide our spinners during that tour, but he will also work with our batsman to help them prepare to play Pakistan's dangerous spin bowlers."
Pakistan have been forced to play their home series at neutral venues since militants attacked the Sri Lankan team in Lahore in 2009.