The school itself determines if they will fully fund the program.
By fully funded, what is normally meant is that they college/university has decided to award athletic scholarships up to the maximum allowable level in that sport. In baseball in Division I, it's 11.7 scholarships (divided over about 38 players on the average.
Just to give you an idea, Funding seems to be a factor that is primarily affected by school size.
For D1 baseball # of scholarships:
School plays D1-A football: 11.2 baseball
School plays D1-AA football: about 9.5 baseball.
D1 with No football program: about 11 baseball.
It's a matter completely up to the institution AND the conference.