The primary objective of this study is to evaluate the long-term safety profile of BG00012 (dimethyl fumarate). Secondary objectives of this study are to evaluate the long-term efficacy of BG00012 using clinical endpoints and disability progression, to evaluate further the long-term effects of BG00012 on multiple sclerosis (MS) brain lesions on magnetic resonance imaging (MRI) scans in participants who had MRI scans as part of Studies 109MS301 (NCT00420212) and 109MS302 (NCT00451451) and to evaluate the long-term effects of BG00012 on health economics assessments and the visual function test.