The agreement exceeds the total value of recent deals signed by Cuban outfielders Yeonis Cespedes (four years, $36 million) and Jorge Soler (nine years, $27 million).
The Cubs and White Sox were among the teams bidding for Puig. He was declared a free agent last week and agent Jaime Torres felt the need to expedite negotiations before July, when new signing limitations for international players are instituted by Major League Baseball.
Puig, 21, is 6-3, 220 and is considered a four- or five-tool prospect.
He hit .330 with 18 home runs and 47 RBIs for the Cienfuegos Elephants in last year's Serie Nacional.