Under the deal, Erat and minor league forward Michael Latta head to Washington in exchange for 18-year-old forward Filip Forsberg, the Capitals' 2012 first-round draft pick.
Erat, a 31-year-old native of the Czech Republic, has amassed 163 goals and 318 assists over 723 career games, all with Nashville, which drafted him with a seventh-round selection in 1999.
Those totals rank him second all-time for the Predators in both goals and assists.
Predators General Manager David Poile made the move as Nashville was percentage points out of the eighth and final playoff spot in the Western Conference.
The Caps, meanwhile, are three points away from a Eastern Conference slot.
Forsberg notched 33 points in 38 games for Leksand of Sweden's second league this season, earning the nod as its top junior player.
"In Filip Forsberg, we are adding one of the top rated young forwards in the world," Poile said.