The Family Court of the State may commit to the custody of the Department any juvenile who is subject to the jurisdiction of such Court and who is delinquent, as that term is defined in § 901 of Title 10; provided, however, that where the adjudication is pursuant to § 1009(e) [repealed] of Title 10, the juvenile shall be committed for the designated statutory period. The Department shall accept the custody of any juvenile so committed to it.