I am looking for exact references for the comparison theorem for the étale fundamental group. I mean the following result:

Theorem(Grothendieck). For a pointed algebraic variety $(X,x)$ over $\mathbb{C}$ there is a canonical isomorphism between the étale fundamental group $\pi_1^{\text{ét}}(X,x)$ and the profinite completion of the topological fundamental group $\pi_1^{\rm top}(X(\mathbb{C}),x)$.

(I am interested in the case when $X$ is nonsingular.)

I could not find this assertion in SGA1 or in the book "Galois Groups and Fundamental Groups" by Tamás Szamuely. Please help!