Grundstrom landed a two-year deal worth $2.6 million through the 2023-24 season, and Andersson agreed to a one-year deal for $750,000.
Grundstrom scored a career-high 15 points in 54 games last season with the Kings. The 24-year-old Swede also scored three goals in Los Angeles' first-round playoff loss to Edmonton.
Grundstrom is a former second-round pick by Toronto. He was traded to the Kings in January 2019 in a package for defenseman Jake Muzzin.
Andersson scored two points in 20 games for Los Angeles last season. He was the seventh overall selection in the 2017 draft by the New York Rangers, who traded him to the Kings in October 2020 for a second-round draft pick.
Also Tuesday, the Kings did not extend a qualifying offer to restricted free agent Brendan Lemieux. The veteran forward and son of former NHL forward Claude Lemieux can sign with any team when free agency begins on Wednesday.
The Associated Press contributed to this report.