The Rays got third baseman Kevin Padlo, and the Rockies got right-hander German Marquez.
In another move, Tampa Bay reached a one-year, $4.75 million deal with free-agent first baseman/outfielder Steve Pearce.
Colorado had an abundance of left-handed-hitting outfielders with the recent signing of Gerardo Parra. Dickerson, who is not yet eligible for salary arbitration, was deemed expendable over the likes of Carlos Gonzalez and Charlie Blackmon.
Dickerson, 26, hit .304 last year with 10 homers and 31 RBIs in 65 games. He was limited early in the season because of plantar fasciitis and then later because of broken ribs he suffered while diving for a ball.
"It's always hard to give up somebody that you've enjoyed watching grow up in the organization and who's obviously a very talented hitter," Rockies general manager Jeff Bridich said during a conference call Thursday night. "You have to give up something to get something. He's got a bright future if he can stay healthy."
He is joining a team that also has a surplus of outfielders. Tampa Bay's roster includes Desmond Jennings, Kevin Kiermaier, Steven Souza Jr. and Brandon Guyer. Barring some sort of move, someone will be headed to the role of designated hitter.
"It's a crowded lineup we have ... but you can never predict how the season will unfold," Rays president of baseball operations Matt Silverman said.
Silverman said Tampa Bay not only addressed a need to bolster a sputtering offense but figures to enter spring training with more depth than usual among position players.
With the Rockies, Dickerson played mostly left field, a spot Jennings has been playing. Jennings has been slowed by injuries past two seasons.
Silverman called Dickerson "an established major league hitter" who potentially fills a hole in the middle of the batting order.
McGee, 29, becomes another piece as the Rockies try to revamp their bullpen. He turned in his best season two years ago when he went 5-2 with a 1.89 ERA and 19 saves in 73 appearances. He started last season on the disabled list after undergoing offseason elbow surgery. He went 1-2 with a 2.41 ERA and six saves in 39 appearances in 2015.
McGee agreed this month to a $4.8 million, one-year contract.
"The departure of Jake leaves a big hole. It will be hard to fill," Silverman said. "It's going to require a couple of guys stepping up ... for us to have the type of lock-down bullpen it's going to take to make the playoffs."
Colorado already brought in former closers to two-year contracts, guaranteeing Jason Motte $10 million and Chad Qualls $6 million. Right-handed reliever Adam Ottavino is expected back sometime around the All-Star break after undergoing Tommy John surgery last May.
"There's an intent here to continue to bombard this organization with impactful pitching," Bridich said. "This is simply another example of that.
"Our goal is to win more games, as many as we can possibly win, and to do that in part by adding high-impact pitching to who we are."
Padlo, 19, spent his first full pro season in Class A. He was a midseason and postseason All-Star in the Northwest League.
Marquez, 20, went 7-13 with a 3.56 ERA at Class A Charlotte.
Colorado designated pitcher Christian Friedrich for assignment. A 28-year-old lefty, Friedrich was 0-4 with a 5.25 ERA in a team-high 68 relief appearances last season.
Pearce, 32, hit .218 with 15 home runs and 40 RBIs for Baltimore last season. He can earn $1.25 million in performance bonuses based on plate appearances: $125,000 each for 400 and 425, and $250,000 apiece for 500, 525, 550 and 575. He also would get a $250,000 assignment bonus if traded.