Clarke, 30, begins his reign as a full-time Australian Test captain hoping to ease into the giant boots of Ricky Ponting, who quit as skipper after the World Cup in April.
Ponting, the world's most successful Test captain with 48 wins, will take the field as the senior statesman and the team's front line 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 to complete their 3-1 Ashes victory.
"My form has not been as good as I would like in Test cricket," Clarke told the travelling Australian media.
"For me, Test cricket is the ultimate, the pinnacle, and I want to be at my best.
"I could not have asked for better preparation, but now I have got to do it when it counts. It's important to make runs every time I bat but I would prefer a hundred in the first Test."
Clarke, regarded as one of the finest players of spin bowling, has scored 4,742 runs in 69 Tests at an average of 46.49 with 14 centuries.
Ponting admitted Australia's Ashes loss when he was captain had affected his batting, and now looked forward to doing well as the team's front line batsman.
"The team's performance had started to play on my mind and it probably dragged my batting down a little bit," Ponting told Cricinfo in a recent interview.
"I have got to score runs that are going to be enough to win for Australia, and that's my main objective for the immediate future."
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 retired, 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 No 1 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 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 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 (September 16-20).