The deal is worth $7 million, The Associated Press reported, citing a person familiar with the negotiations.
The 34-year-old right-hander had been on the Marlins' shopping list since the trade of Dan Uggla freed up money for a veteran starting pitcher.
Vazquez owns a career record of 152-149 with an ERA of 4.26, but is coming off a difficult year in New York, where he went 10-10 with a 5.32 ERA for the Yankees. Even so, the Marlins, Washington Nationals, Chicago Cubs and Colorado Rockies were all known to have shown interest in him this winter.
In fact, there was enough interest, sources told ESPN.com, that Vazquez turned down two multiyear offers -- one of which was believed by other clubs to be potentially worth $20 million over the two years.
Terms of the deal were not disclosed, though it's unlikely it would approach $10 million a year. However, Vazquez has portrayed himself this winter as being more concerned with finding the right fit than the most dollars.
At 34, his preference for a one-year deal would also seem to indicate he has reached the stage of his career where he wants to go year-to-year and assess his future after he sees how he pitches in 2011.
Vazquez is a Type B free agent. He was offered arbitration by the Yankees, apparently with an informal understanding that he wouldn't accept. The Yankees are well aware he had no interest in returning, so offering arbitration assures them of draft-pick compensation when he signs elsewhere.
Information from ESPN.com senior MLB writer Jayson Stark and The Associated Press was used in this report.