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The one who has accomplished the task of division is none other than Vyasa:

The one who has accomplished the task of division (in present Manavantara) is none other than Vyasa:

The reason for division is incapability and short life-period of man near to Kaliyuga: (as I mentioned in this answer

The reason for division is incapability and short life-period of man near to Kaliyuga: (as I mentioned in this answer)

Text 40-41
One perceives this [eternal, itself imperceptibly manifesting] sound, outside the physical sense of hearing and power of vision. The complete of the Vedic sound one employs is an elaboration of this omkâra that from the soul manifests itself in the ether. It constitutes the direct expression of the self-generating Absolute Truth and Supersoul, it constitutes the eternal seed of the Vedas and constitutes the secret of all mantras [see also 7.15: 31, 9.14: 48, 11.14: 34-35, 11.21: 36-40]. Vedas inherently constitutes Rik, Yajur and Sama hymns (even before the division):

These headed down in in every Yugas upto Dwapara and divided at the end of Dwaparayuga:

Text 46
Throughout the four yugas generation after generation, one after the other disciple fixed in his vows received them [these Vedas] by disciplic succession [paramparâ]. They were divided among the prominent sages at the end of Dvâpara-yuga.

Text 47
The brahmin sages, inspired by the Infallible Lord situated in their hearts, came to that dividing among each other of the Vedas when they saw that under the influence of time the intelligence [of the people] diminished, the life span shortened and the strength weakened [see also 1.4: 16-18].

How Vyasa divided Vedas (as I discussed in this answer is explained in further verse:

Text 50
Like someone sorting out gems, he separated the group of mantras in four categories of collections [Samhitâs]: the Rig, Atharva, Yajur and Sâma Veda [see Vedas].

Text 40-41
One perceives this [eternal, itself imperceptibly manifesting] sound, outside the physical sense of hearing and power of vision. The complete of the Vedic sound one employs is an elaboration of this omkâra that from the soul manifests itself in the ether. It constitutes the direct expression of the self-generating Absolute Truth and Supersoul, it constitutes the eternal seed of the Vedas and constitutes the secret of all mantras [see also 7.15: 31, 9.14: 48, 11.14: 34-35, 11.21: 36-40]. Vedas inherently constitutes Rik, Yajur and Sama hymns (even before the division):

Touching the question:

These headed down in in every Yugas upto Dwapara and divided at the end of Dwaparayuga:

ते परम्परया प्राप्तास्तत्तच्छिष्यैर्धृतव्रतैः ।
चतुर्युगेष्वथ व्यस्ता द्वापरादौ महर्षिभिः ॥ ४६॥

Text 46
Throughout the four yugas generation after generation, one after the other disciple fixed in his vows received them [these Vedas] by disciplic succession [paramparâ]. They were divided among the prominent sages at the end of Dvâpara-yuga.

Text 47
The brahmin sages, inspired by the Infallible Lord situated in their hearts, came to that dividing among each other of the Vedas when they saw that under the influence of time the intelligence [of the people] diminished, the life span shortened and the strength weakened [see also 1.4: 16-18].

How Vyasa divided Vedas (as I discussed in this answer) is explained in further verse:

Text 50
Like someone sorting out gems, he separated the group of mantras in four categories of collections [Samhitâs]: the Rig, Atharva, Yajur and Sâma Veda [see Vedas].