The 33-year-old, who was serving a one year jail term for immigration offences, fled the prison even though he was due to be released in under three months, police said.
Davidson had just two months and 15 days left to serve of his sentence for immigration offences after he was caught in April a year ago for using another man's passport on the popular tourist island.
They were believed to have escaped while prisoners were cleaning the yard and preparing for a morning roll call, he said.
Malaysian man, Tee Kok King, 50, is understood to be serving seven-and-a-half- years for drug offences.
Davidson is not only on the run for skipping the last few weeks of his sentence, he is also wanted for drug offences back home in Perth.
Davidson said he lost his passport.
The notorious Kerobokan Prison has been home to many high-profile foreign criminals, including the so-called "Bali Nine" - eight men and a woman from Australia who were convicted in 2006 of smuggling heroin.
Sayed Mohammad Said was the last prisoner seen during morning prayers and again at 6.30am this morning.
When Davidson arrived in Bali in January 2015 he said he spent several months just "partying and boxing" before arousing the suspicion of authorities when he signed into a Kuta guest house under a passport with the name Michael John Bayman - claiming the photo was taken when he was "chubby".
Davidson told Fairfax Media at the time that he would continue to teach boxing inside Kerobokan jail. It gives them something to look forward to.
But he came to the attention of authorities in March past year when he was staying at Rabasta Hotel in Kuta.
Setiawan said they were also investigating the possibility they escaped via the waste tunnel.