Most Major League Baseball teams have Minor League Departments, where the Scouts are. Scouts will visit Triple A teams and High Schools. They take note of talented young players, and meet with other decision making front office personnel. The final decision usually comes from the team Manager, and President/Vice=President of the team. If a team has a 'single' owner, who wants the last say, then of course, this is the final decision.
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If you mean "Who decides on which player goes to the disabled list" that would be the general manager of the team.