The Red Sox have been active at the Winter Meetings, which concluded on Thursday, and unveiled former Arizona Diamondbacks left-hander Miley as the latest of their pitching acquisitions.
Boston also brought Jon Lester, Rick Porcello and Justin Masterson to Fenway Park, as they look to bounce back from their poor defence of their 2013 World Series triumph.
The Red Sox battled to a 71-91 win-loss record in 2014.
Miley, a 2012 All-Star, finished the season with an 8-12 win-loss record for the Diamondbacks, and an earned run average of 4.34.
Meanwhile, the Twins confirmed right-hander Santana had joined the ballclub on a four-year, $54million deal after becoming a free agent.
The 32-year-old signed a one-year contract with the Atlanta Braves prior to the 2014 season after turning down an offer from the Twins, before eventually making the switch to Target Field.
Santana's decision to stay with the Braves paid dividends, as Minnesota's offer 12 months back was a three-year, $33million deal - inferior to what his agent eventually secured for him.
At his third club in as many years after a seven-year stint at the Los Angeles Angels, Santana had a 14-10 record at the Braves in 2014, and an earned run average of 3.95.
He played with the Kansas City Royals in 2013 after moving from the Angels, before one season with Atlanta.