The deal had been in the works for a few days, but was finally agreed to late Thursday night. Myers, 24, will head to the Padres in the deal. He hit .222/.294/.320 over 325 at-bats with the Rays last season. Myers also missed time due to a wrist injury.
The Padres will also receive catcher Ryan Hanigan and pitchers Gerardo Reyes and Jose Castillo in the deal.
Tampa Bay will receive outfielder Steven Souza and pitcher Travis Ott from the Nationals. Souza, 25, hit .345/.427/.577 in 357 at-bats spread over three levels last year.
Washington is set to acquire pitcher Joe Ross from San Diego. The team will also receive infielder Trea Turner in the deal. Turner was a 2014 draft pick, and cannot be traded until midseason, so he's currently considered a player to be named later.