Yamane, who won the 2020 and 2021 J1 titles with Kawasaki, joins previous Japan captain Maya Yoshida with the Galaxy.
The former Samurai Blue captain has not been called up by national team head coach Hajime Moriyasu since the World Cup late last year.
The 34-year-old defender has been a free agent since his departure from Schalke in Germany this summer.
Yoshida has been a free agent since his departure this summer from Schalke, who were relegated from the German Bundesliga at the end of last season.
Japan defender Maya Yoshida is leaving Schalke following their relegation to the Bundesliga's second division, the German club announced Wednesday. The 34-
Made captain early in 2023 with Schalke dead last in the Bundesliga, the 34-year-old Yoshida has been pivotal to the team's surprise resurgence.