The deal buys out the final two years of arbitration for Story, who will reach free agency at 29 in 2021-22.
Story ($11.5 million) and Colorado ($10.75 million) were $750,000 apart when they exchanged salaries in salary arbitration earlier this month.
The 27-year-old Story is coming off a season in which he set career highs in runs (111), batting average (.294) and on-base percentage (.363) while earning $5 million.
He finished with 35 homers and 23 steals, making him the second shortstop in major league history with multiple 30-20 seasons. Alex Rodriguez is the other one.
It also was Story's fourth straight season with at least 20 homers. He's the first shortstop in big league history to begin his career with four consecutive 20-homer seasons.
The Associated Press contributed to this report.