The deal includes an option for a seventh year. The deal is in the range of the six-year extension signed by Indians second baseman Jason Kipnis in April 2014 worth $52.5 million.
Odor is coming off a season in which he hit a career-high .271 with 33 home runs 88 RBIs and recorded a .296 on-base percentage.
Odor is best known for his role in a brawl with Toronto Blue Jays outfielder Jose Bautista. He was suspended eight games for punching Bautista in the face.
Odor played for Venezuela in the recent World Baseball Classic. He turned 23 years old last month.