Key Inclusion Criteria: * Participants with TDT and SCD: * Eligible for autologous stem cell transplant as per investigator's judgment. * Participants with TDT: * Diagnosis of TDT as defined by: * Documented homozygous β-thalassemia or compound heterozygous β-thalassemia including β-thalassemia/hemoglobin E (HbE). Participants can be enrolled based on historical data, but a confirmation of the genotype using the study central laboratory will be required before busulfan conditioning * History of at least 100 milliliter (mL)/kilograms (kg)/year or 10 units/year of packed red blood cells (RBC) transfusions in the prior 2 years before signing the consent or the last rescreening for patients going through re-screening * Participants with SCD: * Diagnosis of severe SCD as defined by: * Documented SCD genotypes * History of at least two severe VOCs events per year for the previous two years prior to enrollment Key Exclusion Criteria: * Participants with TDT and SCD: * A willing and healthy 10/10 human leukocyte antigen (HLA)-matched related donor is available per investigator's judgement * Prior hematopoietic stem cell transplant (HSCT) * Clinically significant and active bacterial, viral, fungal, or parasitic infection as determined by the investigator * Participants with TDT: * Participants with associated α-thalassemia and \>1 alpha deletion, or alpha multiplications * Participants with sickle cell β-thalassemia variant * Participants with SCD: * History of untreated moyamoya syndrome or presence of moyamoya syndrome at screening Other protocol defined Inclusion/Exclusion criteria may apply.