Aramco had earlier said the two Indian and a Bangladeshi workers were missing following yesterday's accident in the waters off the coast of al-Safaniya region, the site of the world's largest offshore oil field.
The remaining 24 crew suffered "limited injuries" but were rescued, Aramco said.
"They (bodies) were all found. We found two of them late yesterday and another one this morning," Eastern Province Coastguard spokesman Col Khaled al-Arqubi was quoted as saying by AFP.
Aramco said a thorough investigation had been launched into the accident, which had not affected its operations.
Saudi Arabia is the world's top oil producer.
Discovered in 1951, al-Safaniya oil field has a capacity of more than 1.2 million barrels per day.