We establish existence and sharp regularity results for solutions to singular elliptic equations of the order u−β, 0 < β < 1, with gradient dependence and involving a forcing term λ f(x, u). Our approach is based on a singularly perturbed technique. We show that if the forcing parameter λ > 0 is large enough, our solution is positive. For λ small solutions vanish on a nontrivial set and therefore they exhibit free boundaries. We also establish regularity results for the free boundary and study the asymptotic behavior of the problem as $${\beta\nearrow 1}$$ we recover the Alt-Caffarelli theory.