Basketball Hall of Famer Magic Johnson, a co-owner of the team, tweeted enthusiastically: "Dodger Nation I am happy to announce we have signed P Zack Greinke, the best pitcher on the Free Agent Market!"
Dodgers' owners, who paid $2.15 billion for the team in March, have added hundreds of millions of dollars in salaries to improve a team that finished second in the National League West with an 86-76 record, eight games behind the eventual World Series champion San Francisco Giants.
Greinke was a combined 15-5 last season, splitting his year between the Milwaukee Brewers and Los Angeles Angels, posting an earned run average of 3.48 and striking out 200 in 212 innings.
The 29-year-old won the American League Cy Young award in 2009, going 16-8 with a league-leading 2.16 ERA for the Kansas City Royals.
Greinke's contract is the largest ever for a right-handed pitcher and, along with Sunday's signing of South Korean left-hander Ryu Hyun-jin, sends the Dodgers' 2013 payroll past $225 million, a Major League Baseball record, mlb.com reported.
Late in the 2012 campaign, the Dodgers made a nine-player blockbuster with the Red Sox, taking on board some $260 million in long-term deals in acquiring Boston's three most expensive players in Carl Crawford, Adrian Gonzalez and Josh Beckett.
Greinke and Ryu, who signed a six-year deal worth a reported $36 million, provide the Dodgers with a potential surplus of starting pitchers, leaving open the possibility of trades with Clayton Kersahw, Chad Billingsley, Aaron Harang, Chris Capuano and Ted Lilly already on the staff.
In 2006, Greinke opened the season on the 60-day disabled list to deal with depression and social anxiety disorder, but he bounced back by winning 13 games in 2008 and claiming the Cy Young award the next season. (Reporting by Larry Fine; Editing by Frank Pingue)