This paper concerns about the approximation by a class of positive exponential type multiplier operators on the unit sphere Sn of the (n + 1)-dimensional Euclidean space for n≥2.We prove that such operators form a strongly continuous contraction semigroup of class (C0) and show the equivalence between the approximation errors of these operators and the K-functionals. We also give the saturation order and the saturation class of these operators. As examples, the rth Boolean of the generalized spherical Abel-Poisson operator ⊕rVtγ and the rth Boolean of the generalized spherical Weierstrass operator ⊕rWtk for integer r≥1 and reals γ, κ∈ (0, 1] have errors ∥⊕rVtγf-f∥X≈ωrγ(f,t1/γ)X and ∥⊕rWtkf-f∥X≈ω2rk(f,t1/(2k))X for all f∈X and 0≤t≤2π, where Xis the Banach space of all continuous functions or all Lpintegrable functions, 1≤p<+∞, on Sn with norm ∥⋅∥X, and ωs(f,t)Xis the modulus of smoothness of degree s>0 for f∈X. Moreover, ⊕rVtγ and ⊕rWtk have the same saturation class if γ=2κ.