The two picks are Vegas' in 2020, and the St. Louis Blues' in 2021, which the Golden Knights had previously acquired. The Kings now own 11 picks in the 2020 NHL Draft, including three second-rounders.
"Alec has been an important part of the organization for a number of years and was a key member of our Stanley Cup teams," general manager Rob Blake said. "We thank Marty for everything he's done for our organization, our fans, and our community."
Martinez, 32, is under contract through the 2020-21 season and carries an annual cap hit of $4 million.
The 6-foot-1 rearguard led the Kings in blocked shots (85) and ranked second in average ice time (21:31 per game) this season. He's contributed one goal and eight points through 41 contests.
Martinez also boasts 64 games of playoff experience. He played an important role in the Kings' 2012 and 2014 Stanley Cup runs and scored the winning goal to clinch the latter championship.
Despite moving a pair of picks, the Golden Knights still own the Pittsburgh Penguins' second-round selection in 2020 and a pair of second-rounders in 2021.