At a news conference Saturday after he signed a $142 million, seven-year contract, Crawford said that when his career is over he hopes he will be mentioned among Red Sox greats such as Ted Williams, Carl Yastrzemski, Jim Rice and Manny Ramirez.
The speedy Crawford's signing as a free agent follows Boston's acquisition of first baseman Adrian Gonzalez from San Diego and gives the Red Sox one of the best lineups in the majors. Crawford said he wanted to stay in the AL East and doesn't mind where manager Terry Francona puts him in the lineup.
"Whatever he wants to do with me is fine," Crawford said.
Center fielder Jacoby Ellsbury, who missed most of the 2010 season with rib injuries, likely will lead off once he fully recovers.
"Our best team is when Jacoby's hitting first," Francona said.
Crawford, a four-time All-Star, hit .307 for Tampa Bay this year while setting career highs with 19 homers and 90 RBIs. A four-time stolen base champion, he swiped 47 bases and led the AL with 13 triples.
General manager Theo Epstein called him a "game changer."
Crawford, who won his first Gold Glove award this year, receives a $6 million signing bonus, with $1 million payable within 30 days of approval and the rest in $1 million installments on the first day of five consecutive months starting in May.
He gets salaries of $14 million next season, $19.5 million in 2012, $20 million in 2013, $20.25 million in 2014, $20.5 million in 2015, $20.75 million in 2016 and $21 million in 2017.
Crawford would earn a $50,000 bonus each time he's an All-Star; $100,000 each for Gold Glove, Silver Slugger and World Series MVP; and $75,000 for league championship series MVP. He would get $200,000 for winning the MVP award, $125,000 for second, $100,000 for third, $75,000 for fourth and $50,000 for fifth.
He also receives a limited no-trade provision. Boston designates 28 teams he can be traded to without his consent and Crawford can eliminate two of them.