Nashville sent a second-round draft pick to the Oilers in exchange for the 26-year-old Russian, Predators General Manager David Poile announced.
Grebeshkov has 19 points, including six goals, in 47 games with the Oilers this year, his third full NHL campaign. He registered career highs in goals (seven) and points (39) a season ago in Edmonton, and has 82 points (16 goals) in 223 career games with the Kings, the Islanders and the Oilers.
He was selected 18th overall by the Kings in the 2002 draft. The 6-foot, 209-pound blueliner represented Russia in the 2010 Olympics, registering an assist while playing in all four of his team's games.