Who divided Vedas into four parts?

According to the Vishnu Purana the original Veda was divided into four parts, and further fragmented into numerous shakhas, by Vishnu in the form of Vyasa, in the  Dvapara Yuga; the Vayu Purana recounts a similar division by Vyasa, at the urging of Brahma. The Bhagavata Purana traces the origin of the primeval Veda to the syllable aum, and says that it was divided into four at the start of Dvapara Yuga, because men had declined in age, virtue and understanding. 

However, if we consider the order of evolution of Vedas, Mahabharata, Srimad Ramayana, etc, we can understand that Vedas were followed by Srimad Ramayana.  And, after a long period Mahabharata came into existence.  

So if we go by these stories, the Vedas should have been remained undivided in the Ramayana era.  

If we read the following issues carefully, we will find that Vedas were already divided into 3 parts by the time  Mahabharata was composed.

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1.   The Sutta Nipāta 1026 (P.303), teachings of Buddha,  mentions about 3 vedas only.

His age is a hundred and twenty years, by clan he is a Bāvarī, upon his body appear three signs, Three Vedas he has mastered all.

We should remember that that Gautama, the Buddha took birth in a Hindu family only. He studied the prevalent literature , observed the prevalent customs and practices , got vexed with the degraded form of spiritual aspects in his times, adopted his own method and finally reached the stage SAT, which Veda described in RV 1.164.46.

Thus, we can infer that by the time Gautama, the Buddha got SELF REALISATION, there were only 3 Vedas.

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2 )       Ramayana, which preceded Mahabharata, contains reference to 3 Vedas only. Sri Raama says Sri Hanuman is well versed in 3 Vedas only.

Sri Hanuma approaches, at the behest of Sugreeva, Sri Rama and Lakshmana to   know the intentions of those two by their conduct, by their semblance, and by their conversation.  

          After listening to him, Sri Rama expresses his opinion on Sri Hanuma to Lakshmana as follows:

न अन् ऋग्वेद विनीतस्य न अ\-\-यजुर्वेद धारिणः |
न अ\-\-साम वेद विदुषः शक्यम् एवम् विभाषितुम् || 

(Kishkinda Kanda 3rd Sarga 28th Sloka)

"Nay...the non-knower of Rig Veda, or the non-rememberer of Yajur Veda, or the non-scholar of Saama Veda... can possibly, or truly speak this way..."

Here, Sri Rama was saying that Sri Hanuma was well versed in Rig, Yajur, Saama Vedas.  So by that time Vedas might have already been divided into 3 parts only but not 4 parts.

3)    While describing the characteristics and bodily signs of Sri Rama to Sita, Sri Hanuma says as follows:

यजुः वेद विनीतः च वेदविद्भिः सुपूजितः |

धनुः वेदे च वेदे च वेद अन्गेषु च निष्ठितः ||   (Sundara Kanda 35th Sarga 14th Sloka)

"He got trained in Yajurveda, the sacrificial Veda. He is highly honoured by those well-versed in Vedas. He is skilled in Dhanurveda, the science of archery, other Vedas and the six limbs of Vedangas."

4)   However, there was a reference to Atharvasirsha in 15th Sarga of Bala Kanda.

इष्टिं तेऽहं करिष्यामि पुत्रीयां पुत्रकारणात् | अथर्वशिरसि प्रोक्तैर्मन्त्रैः सिद्धां विधानतः || १-१५-२

"I will procedurally conduct the ritual contained in the preamble of atharvasirsha with procedural hymns, called putra kaameSTi i.e., the ritual that bestows sons, for your benefit."

However, Sargas 15 to 17 of Bala Kanda are interpolated ones. Hence, this mention of Atharvasirsha in Ramayana also must be interpolated one.

5)  Srimad Bhagavad Gita is a part of Mahabharata.  While explaining the Gita, Sri Krishna says in the "Rajavidya Rajaguhya Yoga" as follows:

पिताऽहमस्य जगतो माता धाता पितामहः।

वेद्यं पवित्रमोंकार ऋक् साम यजुरेव च।।9.17।।

(Srimad Bhagavad Gita 9th Chapter 17th Sloka)

I am both the father and the mother of the universe, I am the Maintainer, the Grandsire, the object of all knowledge, the purifier, the syllable oµ and I am the Rig Veda, Såma Veda and the Yajur Veda.

Srimad Bhagavad Gita was narrated to Arjuna by Sri Krishna, almost at the end of Dwapar Yuga.  Even at time also, the vedas were 3 parts only, but not 4.  The Atharvana Veda is missing.

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If we go through the Manu Smriti, we can find that it mentions about 3 Vedas only.

षट् त्रिंशदाब्दिकं चर्यं गुरौ त्रैवेदिकं व्रतम् । तदर्धिकं पादिकं वा ग्रहणान्तिकमेव वा ॥ १ ॥

ṣaṭ triṃśadābdikaṃ caryaṃ gurau traivedikaṃ vratam | tadardhikaṃ pādikaṃ vā grahaṇāntikameva vā || 1 ||

Duties relating to the Three Vedas should be observed under the Preceptor for thirty-six years, or for half that period, or for a quarter, or precisely till they have been got up.

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Now, coming to the question part - Who divided the Vedas?, we have to take a holistic look to understand the issue.

1. The Rig Veda, composed by various sages at different times, was/is/will be the source of Dharma, for attaining SPIRITUAL heights, for talking anything about Sanatana Dharma.

2. Sama is rasa or essence of Rig-Veda i.e. That is most essential part.

3. The Yagnas mentioned in Rig Veda are mostly mind related, but misunderstood by many and interpreted them to be physical. That is why the Yajur Veda contains physical yagnas.

Even in Ramayana, we can find the importance of Yajur Veda. Sri Rama was described as यजुः वेद विनीतः - trained in Yajurveda.

यजुः वेद विनीतः च वेदविद्भिः सुपूजितः | धनुः वेदे च वेदे च वेद अन्गेषु च निष्ठितः || ५-३५-१४

"He got trained in Yajurveda, the sacrificial Veda. He is highly honoured by those well-versed in Vedas. He is skilled in Dhanurveda, the science of archery, other Vedas and the six limbs* of Vedangas."

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No body divided Vedas into parts. The Sama and Yajur vedas evolved from Rig Veda.

Sama Veda

The Sama Veda, divided into two major parts, first to include the four melody collections, or the Saman, the songs and the latter the Arcika, or the verse books a collection (Samhita) of hymns, portions of hymns, and detached verses. A liturgical text, relating to public worship, all but 75 verses of the total 1875 is derived from the Rig Veda.

Yajur Veda:

The earliest and most ancient layer of Yajur Veda, Samhita includes about 1,875 verses, that are distinct yet borrowed from and built upon the foundation of verses in Rigveda.

The middle layer includes the Satapatha Brahmana, one of the largest Brahmana texts in the Vedic collection and The youngest layer of Yajur Veda text includes the largest collection of primary Upanishads six in number, influential to various schools of Hindu philosophy. These include the Brihadaranyaka Upanishad, the Isha Upanishad, the Taittiriya Upanishad, just to name a few.

For example: The Purusha Suktam appears both in Rig Veda and Shukla Yajurveda

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Now the question of attributing the division of the Vedas to Sage Vyasa crops up.

This was attributed by subsequent writers to Sage Vyasa, narrating him to be an incarnation of Vishnu. Attributing authorship of Puranas might have been done by subsequent writers, in order to give authority to Puranas on par with the Vedas.