This is a Phase 3, randomized (study medication assigned to participants by chance), open-label (identity of study drug will be known to participant and study staff), controlled study which consists of two parts: Part 1 and Part 2. The Part 1 is a pharmacokinetic run-in part, which will be conducted before starting the randomized part (Part 2) of the study and Part 2 is a randomized and open-label study. Part 1 and Part 2 of the study will be conducted in 3 phases: a Pretreatment (Screening) Phase (Up to 14 days before administration of study drug), a Treatment Phase, and a Posttreatment Phase. The Treatment Phase will extend from enrollment (in Part 1) or randomization (in Part 2) until 1 of the following: 1) completion of 3 cycles of therapy, 2) transplantation, if clinically indicated, or 3) progressive disease (PD), whichever comes first. The Posttreatment Phase will continue until death, loss to follow up, consent withdrawal, or study end, whichever occurs first. The end of study is defined as when approximately 60 event-free survival (EFS) events have occurred in Part 2 (death, disease progression, or lack of complete response [CR] or partial response [PR] after 3 cycles of treatment based on blinded independent event review), or the sponsor terminates the study, whichever comes first. Participants in Part 1 will be 1 to less than (<) 18 years old. Participants in Part 2 will be 1 to 30 years old. Participants will be primarily evaluated for pharmacokinetics in part 1 and efficacy (EFS) of ibrutinib in combination with RICE or RVICI background therapy compared to RICE or RVICI background therapy alone in part 2. Participants' safety will be monitored throughout the study.