The 26-year-old forward, who was a restricted free agent, had a salary arbitration hearing Aug. 4.
"They've been so great to me," Grimaldi told The Tennessean after last season. "They've given me a chance to play, to prove myself, to prove I belong. That's all I can ask for. … It's a great place."
Grimaldi had NHL career highs in goals (five), assists (eight), points (13) and games (53) with the Predators last season. He scored three goals in five Stanley Cup Playoff games.
He had 11 points (four goals, seven assists) in 10 games with Milwaukee of the American Hockey League.
Selected by the Florida Panthers in the second round (No. 33) of the 2011 NHL Draft, Grimaldi has 23 points (10 goals, 13 assists) in 90 games with the Predators, Panthers and Colorado Avalanche.