Ponting, the world's most successful Test captain with 48 wins, will take the field as the senior statesman and the team's frontline batsman, but the focus will clearly be on the new skipper.
Clarke's lone Test as captain so far, when he stood in for an injured Ponting, was a forgettable experience as England swept to an innings and 83-run win at Sydney in January.
Ponting began his Test captaincy in Sri Lanka in 2004, leading Australia to a 3-0 sweep, and Clarke will hope for similar results even without retired greats like Shane Warne, Glenn McGrath and Adam Gilchrist.
Dilshan, 34, also took over after the World Cup from Kumar Sangakkara and goes into his first home series as captain hoping to make up for the 1-0 defeat in England earlier in the year.Dilshan will miss the experience of prolific off-spinner Muttiah Muralitharan, Test cricket's leading bowler with 800 wickets, who retired from the longer format a year ago.
Sri Lanka have not won a Test since Muralitharan bade goodbye, losing two and drawing six matches since July 2010.
The first Test at the Galle International Stadium marks the start of a new chapter for both teams looking to climb back in the Test rankings.
Former world number ones Australia have fallen to fifth place, while Sri Lanka, ranked second just a year ago, are fourth behind leaders England, South Africa and India.
With the top four teams due to contest the inaugural world Test championships in England in 2013, both Australia and Sri Lanka will hope to push their claims.
"I think it is going to take time for us to work our way back up the rankings," said Clarke. "But I'm confident with the talent we have and our dedication, I can see us having some success."
Clarke made a confidence-boosting start to the tour, winning the one-day series 3-2 before hitting a century in the drawn three-day practice match in Colombo ahead of the first Test.
Dilshan, meanwhile, was hoping his inexperienced bowling attack would perform well in home conditions where batsmen and slow bowlers have traditionally dominated.
The home squad has four spinners in its ranks, including the unorthodox Ajantha Mendis and leg-spinner Seekkuge Prasanna, 26, who has yet to make his Test debut.
Sri Lanka will be without sling-arm fast bowler Lasith Malinga, who rattled the Australians with his third one-day hat-trick last week, as he has quit Test cricket to concentrate on the shorter forms of the game.
Local media speculated that efforts were being made to convince Malinga to change his mind and make himself available from the second Test onwards.
Rookie paceman Shaminda Eranga, 25, is one of the four young seamers in the squad for the Galle Test alongside Suranga Lakmal, Dhammika Prasad and Chanaka Welegedara.
"There is a lot of variety in our bowling, but we must put up good runs on the board to put the Australians under pressure," said Dilshan. "The key to success is how we bat."
The remaining two Tests will be played in Pallekele (September 8-12) and Colombo (Sept 16-20).