According to Ken Rosenthal of the MLB Network and Fox Sports, the deal is for $7 million and includes a full no-trade clause. The team cannot offer arbitration following the 2011 season.
Vazquez, 34, is a 13-year veteran who was 10-10 with a 5.32 ERA with the Yankees this past season.
A native of Puerto Rico, Vazquez broke in with the Montreal Expos during a time Jeffrey Loria owned the club.
Loria has owned the Marlins since 2002.
A durable right-hander, Vazquez is known for eating up innings, which is something the Marlins are seeking.
Vazquez threw 157 1/3 innings for New York in 2010. From 2005-09, he logged more than 200 innings in each season. And he has surpassed 200 innings nine times.
The Marlins' starters in 2010 were ranked 27th out of 30 teams in total innings pitched.
Vazquez will solidify a spot in the rotation that includes Josh Johnson, Ricky Nolasco, Anibal Sanchez and Chris Volstad.
The Marlins are shaping up to enter Spring Training without a left-hander in their rotation.
Vazquez has won at least 10 games in 11 straight seasons. He was 15-10 with a 2.87 ERA with Atlanta in 2009.
Securing Vazquez is yet another offseason pickup for Florida. The club recently signed catcher John Buck to a three-year contract. And they've made three trades that have added depth to their bullpen.
Their biggest trade was dealing Dan Uggla to the Braves for Omar Infante and Mike Dunn.
Joe Frisaro is a reporter for MLB.com. Follow him on Twitter @JoeFrisaro. This story was not subject to the approval of Major League Baseball or its clubs.