No, E-Verify does not replace the legal requirement to complete and retain Form I-9. E-Verify verifies the employment authorization of new hires based on the information they provide on Form I-9. You still must retain and store Form I-9 in either paper, electronic, or microfilm/microfiche format for as long as the employee works for you, plus the required retention period.
See The Handbook for Employers: Guidance for Completing Form I-9 (M-274) for more information on retention of Form I-9.