The deal was announced two days after the Rays agreed to part with Myers in a move that president of baseball operations Matt Silverman said will make Tampa Bay "more competitive for 2015 and beyond."
Tampa Bay acquired five players. Catcher Rene Rivera, pitcher Burch Smith and minor league first baseman Jake Bauers come over from the Padres, and Souza and minor league pitcher Travis Ott from the Nationals.
Myers, catcher Ryan Hanigan and minor league pitchers Jose Castillo and Gerardo Reyes were dealt to San Diego. Washington received minor league pitcher Joe Ross and a player to be named from the Padres.
"Trading Wil Myers was not an easy decision, but we are very excited about the talent coming back our way, and this deal has potential to improve our team on both sides of the ball," Silverman said.
Myers, then Kansas City's top prospect, was acquired by Tampa Bay in a trade that sent pitchers James Shields and Wade Davis to the Royals two years ago. He hit .293 with 13 homers and 53 RBIs in 88 games on the way to being selecting AL Rookie of the Year, then struggled in 2014 when a broken right wrist limited him to playing 87 games and batting .222 with six homers and 35 RBIs.
Silverman said during last week's winter meetings that he expected Myers to rebound with a big season. On Friday, he rejected the notion the Rays appeared to have given up on the 24-year-old slugger.
"This isn't about giving up on Wil Myers. This is about a trade to make this team better," the executive said, adding that Myers' vast talent enabled the Rays to make a deal that can help the team both offensively and defensively.
To clear room on the 40-man roster for Rivera, Smith and Souza, the Rays designated right-hander Brandon Gomes for assignment.
Souza spent most of last season at Triple-A Syracuse, where he hit .350 with 18 homers, 75 RBI's and 26 stolen bases.
The 25-year-old was a September call-up for the Nationals, best known for a sprinting, diving catch in left field for the final out of Jordan Zimmermann's no-hitter in the NL East champs' regular-season finale.
Souza did not make the team's post-season roster, however, he was expected to compete for a spot on the bench behind starters Bryce Harper, Jayson Werth and Denard Span next season.
Silverman said the Rays have not decided where they'll play Souza, who has experience at all three outfield positions and third base.
"He's an outfielder with tremendous talent," Silverman said. "We expect him to be a mainstay in our lineup for years to come."
Rivera, 31, batted .252 with 11 homers and 44 RBI's while making a career-high 85 starts at catcher for the Padres in 2014.
Smith is a 24-year-old right-hander who was 15-11 with a 3.71 ERA in 48 appearances over parts of four minor league seasons. He spent 2014 with Triple-A El Paso, where he made two April starts before missing the remainder of the years with a forearm injury.
Bauers, a 19-year-old prospect, hit .296 with eight homers and 64 RBI's in his first full pro season with Class-A Fort Wayne.
Ott, also 19, split time between Class-A Auburn and Hagerstown last season, going 1-4 with a 3.993 ERA over 13 starts.