The principal object of this paper is to provide the composition of Saigo fractional integral operators with different forms of Voigt functions. An alternative explicit representation of the generalized Voigt function in terms of Laplace integral transform is shown and the relations between the left-sided and the right-sided Saigo fractional integral operators are established with the $_1F_1$-transform and the Whittaker transform, respectively. Many interesting results are deduced in terms of some relatively more familiar hypergeometric functions in one and two variables.