The team announced the deal with the No. 5 pick in the draft on Wednesday. Cousins can earn about $7 million in the first two years of the deal, and the Kings have separate team options for the third and fourth seasons.
Cousins averaged 15.1 points, 9.8 rebounds and 1.8 blocks as a freshman at Kentucky. He was one of five Wildcats taken in the first round of the draft.
The Kings are counting on Cousins to be the dominating inside presence they have been lacking in recent years.