Kansas City was 12th among 14 AL teams in runs last season and added power last month, obtaining first baseman Mike Jacobs from Florida.
The switch-hitting Crisp gives the Royals speed at the top of the lineup and a superb defender in center field who has World Series experience.
"The speed aspect of it was very important," Royals general manager Dayton Moore said. "I've talked many times about the importance of a balanced lineup, speed at the top and the bottom, and Coco certainly gives us that."
The 29-year-old was the subject of trade rumors for much of last season following the emergence of rookie Jacoby Ellsbury.
The two split time in center, with Crisp hitting .283 with seven homers and 41 RBIs in 98 games. He also stole 20 bases in 27 attempts, the third straight season he's reached the 20-steal mark.
Ellsbury hit .280 with nine homers and 47 RBIs last season, proving to the Red Sox that he's ready to be an everyday player. Boston also gains financial savings by trading Crisp, who's due to make $5.75 million next season in a deal that includes an $8 million club option for 2010 with a $500,000 buyout.
"He played through injuries. He played hard," Red Sox general manager Theo Epstein said of Crisp. "With the emergence of Jacoby Ellsbury, we felt like we would be able to find a [backup] outfielder on the market easier than we would find a valuable member of the bullpen."
The Royals got Ramirez, a 27-year-old righty, in a trade with Colorado before last season. They were so impressed with his stuff that they projected him to be their closer.
With a fastball that reaches the mid-90s mph, Ramirez is a power pitcher who seems suited for the late innings. He was one of the primary set-up men for closer Joakim Soria and flourished in that spot, going 3-2 with a 2.64 ERA and 70 strikeouts in 71 2/3 innings.
"He's very quietly had a tremendous amount of success in the major leagues over the last 2½ years," Epstein said.
"It's a new experience for me to be able to play on a contending club. I know that Boston is going to be in it, as they have in previous years," Ramirez said, speaking through a translator on a conference call. "I couldn't be happier right now. I'm ecstatic."
Masterson was 6-5 with a 3.16 ERA in 36 games as a rookie last season -- 4-3 with a 3.67 ERA in nine starts. As a reliever, he was 2-2 with a 2.36 ERA and worked nine postseason games with a 1.86 ERA and no decisions.
"[He] gives us the flexibility to start Masterson," Epstein said. "Ramirez potentially could replace Masterson in the 'pen."
Boston traded for Crisp after his breakout season -- .333, 15 homers, 69 RBIs -- with Cleveland in 2005. But a broken finger derailed Crisp's first year in Boston and Epstein said his offense never fully recovered.
Crisp has always been a superb fielder and picked up his offense the last half of 2008, hitting .315. He also hit .417 (10-for-24) in the playoffs, driving in the tying run in the eighth inning to complete Boston's comeback from a 7-0 deficit in Game 5 of the AL Championship Series against Tampa Bay.
"I play hard and pretty much stay within myself," said Crisp, a career .280 hitter. "I know what I can and cannot do, and with that I think it makes me a pretty good ballplayer. And to help the team, besides stepping on the field, I can hopefully bring a presence into the clubhouse that will help us win, the attitude of winning."
Epstein said the Red Sox hope to replace Crisp with a right-handed fourth outfielder who can play center. He probably will look outside the organization.
The addition of Crisp could signify more moves for the Royals, as well.
Crisp is expected to be the starter in center and Jose Guillen, the highest-paid player in franchise history, is locked in at right. That means Kansas City will have to find a way to get enough playing time for David DeJesus and Mark Teahen.
The loss of Ramirez also creates a hole in the middle of the bullpen that will likely need to be filled from outside the organization.
"I think it's safe to assume there's possible changes, but if we have to begin the season with the core group we finished the season with, it can be managed easily," Moore said.