The agreement is subject to Crawford passing a physical, the person said Wednesday night. The person spoke on condition of anonymity because the deal was not yet final.
Crawford's deal was first reported by The Boston Globe on its website.
A four-time All-Star and a first-time Gold Glove winner this year, Crawford hit .307 this year for Tampa Bay and set career highs with 19 homers and 90 RBIs. A four-time stolen base champion, he also swiped 47 bases and led the AL with 13 triples.
He joins a powerful lineup that already includes designated hitter Ortiz and helps fill some of the production lost by the departure of catcher Victor Martinez and possible departure of Adrian Beltre. Crawford figures to play left field in an outfield that projects to have Mike Cameron or Jacoby Ellsbury in center and J.D. Drew in right.
The Los Angeles Angels had been considered the front-runner to land Crawford, and Yankees general manager Brian Cashman met with him on Tuesday night.
The average annual value of Crawford's contract, $20,285,714, is the seventh highest among current players, trailing only those of Alex Rodriguez ($27.5 million), Ryan Howard's deal that starts in 2012 ($25 million), CC Sabathia and Joe Mauer ($23 million), Johan Santana ($22,916,667) and Mark Teixeira ($22.5 million).
It is the 10th-largest contract in baseball history behind Alex Rodriguez's $275 million and $252 million deals, and agreements for Derek Jeter ($189 million), Mauer ($184 million), Teixeira ($180 million), Sabathia ($161 million), Manny Ramirez ($160 million), Troy Tulowitzki ($157.75 million) and Miguel Cabrera ($152.3 million).