Murali's appointment comes after the Kangaroos had last month appointed former Lankan batsman Thilan Samaraweera to work with the Test hopefuls.
Smith said that the 44-year-old had already begun to work with Australia's spinners in their training sessions here, where the team arrived last weekend.
"Murali's got a lot of experience in Sri Lanka. He took a truckload of wickets. It's great to have someone like that helping our spinners in this series - to give us that insight. He's been really good around the group so far and he's enjoying his time with us," Smith was quoted as saying by espncricinfo.
Australia had previously hired the world's leading wicket-taker in a short-term consulting role ahead of their Test series against Pakistan, in the UAE, in 2014.
Both off-spinner Nathan Lyon and left-armer Steve O'Keefe, who are on the Sri Lanka tour, had worked with Murali on that occasion. He has had two training sessions with the Australia team in this stint so far.
"Murali has been fantastic around the guys. Murali loves the game of cricket, so I'm sure he'd work well with other teams as well - he's a fantastic coach," Australia coach Darren Lehmann said.
The first of the three Tests will begin in Pallekele on July 26 while the second and the third match will be played respectively at Galle and Colombo.
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