Minier, who ranks No. 4 on MLB's International Prospect list, is a switch-hitting infielder with power from both sides of the plate.
The 16-year-old is currently a shortstop, but could move to third base. He's already 6-foot-2 and 190 pounds.
"That was the big one that we were chasing," Twins assistant general manager Rob Antony said. "We like his bat, and we like his power."
Minier is eligible to play in the Minors next season, but the contract begins in 2012. He's free to work out with the organization's Dominican Summer League this year, but can't play in any games.
In accordance with the new Basic Agreement, the international system now operates with money pools and penalties for teams that exceed their pools. For the 2012-13 signing period, every team will have the same pool of $2.9 million. Starting in 2013-14, the pools will be based on the prior season's winning percentages, with a range of approximately $1.7 million to $4.8 million.