Extension Study to Evaluate Safety and Efficacy of Natalizumab in Japanese Participants With Relapsing-Remitting Multiple Sclerosis

Key Inclusion Criteria: * Ability to understand the purpose and risks of the study and provide signed and dated informed consent and any authorizations required by local law. * Subjects who participated in and completed all protocol-related evaluations through Week 24 of Study 101MS203 (NCT01440101). * Subjects participating in study 101MS204 (NCT01416155) participated either in the open label pharmacokinetics-pharmacodynamics study or placebo-controlled study of natalizumab 300 mg q4wks (parts A and B of study 101MS203, respectively). * Subjects of childbearing potential must practice effective contraception during the study and be willing and able to continue contraception for 12 weeks after their last dose of study treatment. * Must be willing to remain free from concomitant immunosuppressive or immunomodulatory treatment (including interferon beta \[IFNβ\] and long-term systemic corticosteroids) for the duration of the study. Key Exclusion Criteria Medical History * Any significant change in medical history since Study 101MS203 (NCT01440101), including laboratory tests, or current clinically important condition that in the opinion of the Investigator would have excluded the subject's participation in the previous study. The Investigator must re-review the subject's medical fitness for participation and consider diseases that would preclude treatment. * Subjects from Study 101MS203 (NCT01440101) who discontinued study treatment due to an adverse event. * Subjects who are determined to be persistently positive for anti-BG0002 antibodies based on prior testing. Treatment History * Treatment with any of the following medications between last dose of study treatment in Study 101MS203 (NCT01440101) and the start of this study: intravenous immunoglobulin (IVIg), plasmapheresis, cytapheresis, immunosuppressant medications (e.g., mitoxantrone, azathioprine, cyclophosphamide, methotrexate, cyclosporine, FTY720), immunomodulatory medications (including IFNβ and glatiramer acetate \[GA\]) total lymphoid irradiation, cladribine, T-cell or T-cell receptor vaccination, any murine protein, any other therapeutic monoclonal antibody, or any 4-aminopyridine or related products. Miscellaneous * For female subjects, unless postmenopausal for at least 1 year or surgically sterile (does not include tubal ligation), unwillingness to practice effective contraception, as defined by the Investigator, during the study. Women considering becoming pregnant while on study are to be excluded. * Female subjects who are currently pregnant or breast feeding, including subjects whose pregnancy test is positive at Week 0. * Unwillingness or inability to comply with the requirements of this protocol, including the presence of any condition (physical, mental, or social) that is likely to affect the subject's ability to comply with the study protocol. * Subjects with any other condition, clinical finding, or reason that in the opinion of the Investigator and/or the Sponsor makes the subject unsuitable for enrollment into the study. NOTE: Other protocol defined Inclusion/Exclusion criteria may apply.