The agreement, which includes a partial no-trade clause, is subject to Crawford passing a physical.
Crawford's deal was first reported by The Boston Globe on its Web site.
• LEMIRE: Balance of power shifts in AL
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.
Crawford joins a powerful lineup that already includes designated hitter David Ortiz and newly acquired first baseman Adrian Gonzalez 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.
With Crawford and Gonzalez, the Red Sox hope to replicate the power threat they had when Ortiz and Manny Ramirez helped them win World Series titles in 2004 and 2007. Crawford batted .324 last season at Fenway Park.
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).