Greinke, 29, was considered the top free-agent pitcher on the market. He ended last season with the Los Angeles Angels.
Greinke, who won the 2009 AL Cy Young Award with Kansas City, joins a staff that includes 2011 NL Cy Young Award winner Clayton Kershaw.
"We were definitely hoping for Zack," said NBA legend Magic Johnson, a partner in Guggenheim Baseball Management, which bought the Dodgers last spring. "Zack is a proven winner. When you put him together with Clayton, man, we feel really good."
The Dodgers introduced South Korean left-hander Ryu Hyun-jin, who has a $36 million, six-year deal, at a news conference. Ryu will be the first player to go directly from the Korean league to the North American major leagues.