The deal carries an average annual value of $850,000.
Shore, who was a pending restricted free agent, gets a yearly raise of $150,000 after inking a one-year pact with Edmonton for the league minimum in January. He produced five goals and four assists in 38 games with the Oilers this season.
The center, who turns 27 on July 19, began his career with the Dallas Stars, playing three-plus seasons with the club that drafted him 61st overall in 2012. He played for the Anaheim Ducks and Columbus Blue Jackets in 2019-20, notching five goals and seven assists over 45 contests.