The men were picked up on August 9 near the Marshall Islands by a Taiwanese fishing boat, said Eugene Muller, manager of Koo's Fishing, in the islands' capital of Majuro.
"They were skinny and hungry when they were picked up last week but otherwise healthy," he said.
The men reportedly survived by catching seabirds and drinking rainwater.
However, details of the fishermen's ordeal were sketchy because of communication problems between the Chinese-speaking fishing boat crew and the Mexicans, he said.
Salvador Ordonez Vasques, Jesus Eduardo Vidana Lopez and Lucio Randon Bacerra from the Pacific coastal town of San Blas in central Mexico had been adrift in a small fishing boat with two disabled outboard motors.
The Taiwanese fishing vessel that rescued the men is expected to return to Majuro to offload its catch of tuna - and the Mexican fishermen - in about two weeks.
Muller said the same fishing boat had picked up two drifting fishermen from Kiribati in March after they had been lost at sea for more than two months.
He said he had contacted the Marshall Islands government to ask the Mexican embassy in New Zealand, which handles relations with the Marshall Islands, to help get the three men home.