According to SB 12.6.50 it appears Vyāsa (Kṛṣṇa Dvaipāyana) only rearranged the Vedic mantras into four parts:
50. Just as (out of a heap of mixed up) precious stones of the same kind are assorted and kept in separate heaps, he (Vyāsa) selected and classified the Vedic Mantras as belonging to the category of the Ṛg, Atharvan, Yajus, and Sāman and thus compiled four Saṃhitās or collections out of those (formerly mixed up) Mantras.
So who classified the various brāhmaṇas, āraṇyakas and upaniṣads into the four Vedic branches? Was it Vyāsa's disciples?