Terms of the deal were not disclosed.
Kershaw, 23, won the NL Triple Crown in the 2011 campaign, by virtue of his league-best wins (21), strikeouts (248) and earned run average (2.28) in 33 starts. He was named the 2011 NL Cy Young Award winner for his efforts.
In addition to his pitching excellence, Kershaw aided his teammates in the field, netting him a Gold Glove award for the league's best defensive pitcher.
During his four years in the major leagues, all with the Dodgers, Kershaw has posted a 47-28 record with a 2.88 ERA in 118 games (116 starts). In five postseason appearances over two seasons, 2008 and 2009, the southpaw is 0-1 with a 5.87 ERA.
Kershaw was drafted 7th overall by the Dodgers in the 2006 MLB draft.