The series, which opens at a traditionally spin-friendly venue in Galle on August 31, will mark the start of Clarke's full-time reign captain since taking over from Ricky Ponting after the World Cup.
Clarke said a 3-2 success in the one-day international (ODI) series against the hosts would stand his side in good stead going into the Test matches.
"I think it's been really good to get some cricket under the belt in these conditions," Clarke said after his team's four-wicket defeat in the fifth and final ODI in Colombo on Monday night.
"Looking at the result, I would imagine that the wickets are going to turn throughout the series and we are going to be facing a lot of spin. We need to be prepared for that.
"We have to be at our best as a batting group. We are fortunate we've got a lot of experience in our batting group but we have to make some big scores."
Sri Lanka will be without match-winning fast bowler Lasith Malinga for the Test series, but Clarke said the hosts still had the bowling resources to test his batsmen.
Malinga, who became the first bowler to take three hat-tricks in one-day internationals, has already retired from Test cricket in a bid to prolong his career in limited-overs cricket.
"I think a few of the boys are happy we don't face him [Malinga] in the Test series," said Clarke, who was named man of the one-day series for scoring 242 runs in the five matches.
Man of the match Malinga dismissed Mitchell Johnson, John Hastings and Xavier Doherty off successive balls to spark a dramatic collapse which saw Australia lose their last five wickets for just one run.
Australia were bowled out for 211 before Sri Lanka achieved the target with three overs to spare.
"I'm sure Sri Lanka are going to have a good attack in the conditions we're playing in. I'd be surprised if they don't play two spinners at least," said Clarke.
Sri Lanka are likely to field the unorthodox spinner Ajantha Mendis and the left-arm spinner Rangana Herath in the Tests.
Australia will play a three-day practice match against a Sri Lanka Board XI in Colombo starting Thursday before the Test series.