The restricted free agent agreed to the deal Friday.
Palmieri had 10 goals and 11 assists in 42 games with the Pacific Division champion Ducks last season, his first full NHL campaign. He added five points in Anaheim's first-round playoff loss to Detroit, tying for the team lead with three goals.
Palmieri has 15 goals in 70 NHL games over three seasons with the Ducks, who drafted the American forward in the first round in 2009.
The Ducks are hoping he'll assume a more prominent offensive role next season after the departure of goal-scorer Bobby Ryan, who was traded to the Ottawa Senators earlier this month.