The East Timor police arrested Indian Sayed Muhammad, sentenced to 14 years for drug-trafficking, and Bulgarian Dimitar Nikolov, who was serving a seven-year sentence for fraud, from a luxury hotel in East Timor's capital Dili.
Bali police's vice-director of Special Criminal Investigation, Ruddi Setiawan, said Indonesian authorities had arranged to pick the men up soon.
The four prisoners were discovered missing from Kerobokan jail at the 8am head count on Monday.
He said the prisoners used a drain installed in 1992 to escape, eventually emerging from a muddy hole measuring just 50 cm by 75 cm at its opening.
Bali police were en route to Dili to return the men to Kerobokan.
Mr Hutabarat said prisoners had been sent down the thirteen metre tunnel, which prison authorities had previously assumed was a septic tank outside the jail clinic.
According to the Sydney Morning Herald they entered East Timor via a boat from the Indonesian island of Alor in East Nusa Tenggara.
Shaun Davidson is still on the run a day after escaping from the a waste tunnel.
Authorities have admitted they don't know where the prisoners' passports are.
"We want it done as soon as possible", Surung Pasaribu told reporters on Tuesday.
Kerobokan Prison Governor, Tony Nainggolan said officials believe it took them more than a week to dig the tunnel.
The four inmates escaped their cells through the ceiling, Mr Pasaribu said, and some of the CCTV cameras failed to capture them as they were broken.
He had an outstanding warrant in Australia for drug charges and had told fellow prisoners he meant to "do something" before his sentence ended to avoid being deported back to Australia.
Yudith said two other inmates who remained at large were still being hunted down.
Kerobokan prison was built for 300 prisoners but holds more than 1,300 inmates at present, many of them sentenced for drug offences on the popular tourist island.