Last[Last[Position[list, Min[Select[list, NonNegative]]]]]
for just the value- thanks
Position[list, Min[Select[list, NonNegative]]]
Nevermind, solved it.
a = Range[-5, 5, 1] /. x_ /; x < 0.0 -> 999999999 b = Min[a] position = Last[Last /@ Position[a, _?(# == b &)]]