Broad sat out of the first two Tests and will now return to the scene of this Test debut in 2007.
An unassailable 2-0 series lead means that England will shove South Africa down to third in the ICC Test Championship.
Dananjaya, who came under scrutiny when he was reported for a suspect bowling action during the Galle Test, will have his action assessed in Brisbane.
Root scored his 15th Test hundred, and second in Asia, as the visitors ended the day on 329/8 at Pallekele.
Atherton credited Root’s aggressive approach for showing the way to counter Sri Lanka’s spinners.
England reached 324 runs for the loss of nine wickets against Sri Lanka, stretching their lead to 278 runs.
Should they succeed at Pallekele, England will have claimed their first away Test series win since the 2-1 success in South Africa in 2015-16.
Seeing as he is eligible to play until the results of tests on his action are out, the hosts have backed him to succeed.
Sri Lanka will be without the retired Rangana Herath and regular captain Dinesh Chandimal who suffered a groin staring during the Galle Test.
England captain Joe Root has backed Buttler for a good run at one-down, while Jonny Bairstow looks set to miss out at Kandy.