The tunnel is just 40cm in diameter and ran from behind the jail clinic, under the jail wall to the outside, ironically just near the guard tower.
Jail officials are currently at the scene, using a hose to suck water from the tunnel.
"We are still working to chase them. We have also made a report to the police," Pasaribu said.
"We found that they have gone this morning. We found a hole behind the clinic to the outside, underground. We allege that they escape through the underground hole," he said.
The other three escapees are Dimitir Nikolon Ilev, a Bulgarian, on charges of ATM scamming, Sayed Muhammad Said, Indian, drug smuggler, and Tee Kok Ming, from Malaysia , on drug charges.
Davidson, 32, from Subiaco in Perth, was convicted of using another man's passport in Bali. At the time he was wanted on drugs charges in WA.
Badung Police chief, Yudith Satriya Hananta, said police had put a ban on any of the four escapees from exiting Bali through any travel gates.
And inmates in their prison block were being questioned.
"We have received a report about the four inmates escaping from the prison this morning," Hananta said.
"We conducted some action, as questioning some inmates in the same block with them and the prison guards on duty last night.
"We have spread the photos of those foreign inmates that have escaped and we are chasing them now," he said.
""We have co-ordinated with all police across Bali, the airport and closes all gates in and out of Bali."