This is a Phase II, open-label (all people involved know the identity of the assigned drug) and single arm study. The study will consist of a screening period of maximum 8 weeks, an initial treatment period of 48 weeks, a post week 48 treatment extension period of 4 years (Cohort 1 only), and a 4 week follow-up (cohort 2 only) period. Participants who withdraw from the trial on or before the Week 48 visit or subjects with ongoing (serious) adverse events ([S]AEs), laboratory abnormalities, or viral load increase at the last on-treatment visit in the extension, will be seen for a follow-up visit 4 weeks later. The initial 48-week treatment period will be structured into 2 age Cohorts; Cohort 1 (Aged greater than or equal to [>=] 12 to less than [<] 18 years) and Cohort 2 (Children Aged >= 6 to < 12 years). The trial is designed to evaluate the steady-state pharmacokinetic (PK) profile (based on intensive PK analysis) and the short-term safety and antiviral activity of rilpivirine (RPV). Participants will receive RPV 25 milligram (mg), or weight-adjusted dose orally once daily for 240 weeks when administered in combination with 2 nucleoside/nucleotide reverse transcriptase inhibitors (NRTIs). The trial will also evaluate long-term (48 weeks and 240 weeks [Cohort 1]) safety, efficacy, and pharmacokinetics of rilpivirine in combination with the background regimen of 2 NRTIs. Patients safety will be monitored throughout the study and during the follow up visits.