The arrests came after Thanachart Bank staff reported to police on Dec 2 that thieves cut open an ATM and made off with boxes containing 500-baht and 100-baht notes.
Police used surveillance camera footage in the area to identify the three suspects and followed their trail.
The trio were tracked down and arrested at a hotel in Bangkok's Makkasan area and taken to Kathu police station for questioning.
The suspects - a Colombian, a Mexican and another foreigner of unidentified nationality - went through an immigration checkpoint at Krabi airport on Nov 30, where they rented a car and headed to Phuket.
When they arrived on the island, they stopped at the Thai Watsadu hardware store in Phuket's Thalang district to buy tools which police say were to be used in the robbery.
Police found a gas cylinder and a pair of gloves at the scene.
After the robbery, the suspects went back to Krabi and returned the rented car before boarding a bus to Bangkok on Dec 3.
They later checked in at the hotel in Makkasan, where they were arrested.
Police said the suspects confessed and were charged with conspiring to commit robbery.