The agreement includes a $28 million signing bonus, Genske said Tuesday.
Olivera, who turns 30 next month, drew interest from several other teams, including the Braves, Padres, Marlins and Yankees.
MLB.com was first to report Olivera's deal with Los Angeles.
Olivera will join a crowded Dodgers infield that already features second baseman Howie Kendrick and shortstop Jimmy Rollins. Olivera likely will have the best chance to play third base, where Juan Uribe is expected to start.
Los Angeles also has Cuban infielder Alex Guerrero, who has impressed this spring, and highly touted shortstop prospect Corey Seager.
Information from The Associated Press was used in this report.
Cuban Infielder Olivera Signed By Dodgers
MLB.com reporter Jesse Sanchez discusses why the Dodgers signed 29-year-old Cuban infielder Hector Olivera to a six-year deal.