The Kings on Thursday also re-signed defenseman Vincent LoVerde and forwards Jordan Weal, Andrew Crescenzi and Nic Dowd.
Shore got a two-year, $1.2 million deal after making his NHL debut last season. He appeared in 34 games for the Kings.
Shore scored seven points and won a team-best 53.8 percent of his faceoffs for the Kings before winning the Calder Cup with the AHL's Manchester Monarchs.
Weal, Crescenzi, Dowd and LoVerde also played extensively for the Kings' championship-winning AHL affiliate. Weal was the Calder Cup playoffs MVP.
LoVerde got a two-year contract worth $1.15 million, and the other three signed one-year deals.