It's the biggest deal ever for a right-handed pitcher, a report on the Dodgers' website said, and ranks only behind the $161 million, seven-year contract the New York Yankees gave CC Sabathia, a left-hander, in total dollars
Greinke, 29, the American League's Cy Young Award winner in 2009, went 15-5 with a 3.48 ERA in 34 starts between Milwaukee and the Los Angeles Angels this past season.
He is 70-43 with a 3.39 ERA since 2008.
"Dodger Nation I am happy to announce we have signed P Zack Greinke, the best pitcher on the Free Agent Market!" Dodgers part-owner Magic Johnson alerted followers of his Twitter account.
Paying Greinke will push Los Angeles' projected payroll for the 2013 season above $225 million, which would be the highest in major league history.