We complete the procedure of extracting parton distribution functions (PDFs) using large momentum effective theory at leading power accuracy in the hadron momentum. We derive a general factorization formula for the quasi-PDFs in the presence of mixing and give the corresponding hard matching kernel at O(alpha(s)), both for the unpolarized and for the polarized quark and gluon quasi-PDFs. Our calculation is performed in a regularization-independent momentum subtraction scheme. The results allow us to match the nonperturbatively renormalized quasi-PDFs to normal PDFs in the presence of mixing and therefore can be used to extract flavor-singlet quark PDFs as well as gluon PDFs from lattice simulations.