The Buddha in Hinduism is sometimes viewed as an Avatar of Vishnu. In the Puranic text Bhagavata Purana, he is the twenty-fourth of twenty-five avatars, prefiguring a forthcoming final incarnation. Similarly, a number of Hindu traditions portray Buddha as the most recent (ninth) of ten principal avatars, known as the Daśāvatāra (Ten Incarnations of God). The Buddhist Dasharatha Jataka (Jataka Atthakatha 461) represents Rama as a previous incarnation of the Buddha as a Bodhisattva and supreme Dharma King of great wisdom.
Buddha's teachings deny the authority of the Vedas and consequently Buddhism is generally viewed as a nāstika school (heterodox, literally "It is not so") from the perspective of orthodox Hinduism.
Views of the Buddha in Hinduism
Due to the diversity of traditions within Hinduism there is no specific viewpoint or consensus on the Buddha's exact position in reference to the Vedic tradition:
In the Dasavatara stotra section of his Gita Govinda, the influential Vaishnava poet Jayadeva Goswami (13th C AD) includes the Buddha amongst the ten principal avatars of Vishnu and writes a prayer regarding him as follows:
O Keshava! O Lord of the universe! O Lord Hari, who have assumed the form of Buddha! All glories to You! O Buddha of compassionate heart, you decry the slaughtering of poor animals performed according to the rules of Vedic sacrifice.
Vivekananda: May he who is the Brahman of the Hindus, the Ahura Mazda of Zoroastrians, the Buddha of Buddhists, the Jehovah of the Jews, the Father in Heavens of Christians, give strength to you to carry out your noble ideas!
Radhakrishnan: If a Hindu chants the Vedas on the banks of the Ganges, ... if the Japanese worship the image of Buddha, if the European is convinced of Christ's mediatorship, if the Arab reads the Koran in the mosque ... It is their deepest apprehension of God and God's fullest revelation to them.
Reaction to reforms instigated by the Buddha within Hinduism
Buddhism finds favor in contemporary Hindutva movement, with Lama Tenzin Gyatso, the 14th Dalai Lama being honored at Hindu events, like the Vishva Hindu Parishad's second World Hindu Conference in Allahabad in 1979.
In Hindu scriptures
The Buddha is described in important Hindu scriptures, including almost all the Puranas. However, not all of them refer to the same person: some of them refer to other persons, and some occurrences of "buddha" simply mean "a person possessing buddhi". Most of them, however, refer to the founder of Buddhism. They portray him with two roles: preaching views in order to delude demons or others, and criticizing animal sacrifice as prescribed in the Vedas. A partial list of Puranas mentioning the Buddha is as follows:
- Harivamsha (1.41)
- Vishnu Purana (3.18)
- Bhagavata Purana (1.3.24, 2.7.37, 11.4.23) 
- Garuda Purana (1.1, 2.30.37, 3.15.26)
- Agni Purana (16)
- Narada Purana (2.72)
- Linga Purana (2.71)
- Padma Purana (3.252) etc. (Dhere Ramchandra Chintaman) 
Another important scriptures that mentions him as an Avatar is Rishi Parashara's Brihat Parashara Hora Shastra (2:1-5/7).
He is often described as a yogi or yogācārya, and as a sannyāsi. His father is usually called Śuddhodhana, which is consistent with the Buddhist tradition, while in a few places the Buddha's father is named Añjana or Jina. He is described as beautiful (devasundara-rūpa), of white or pale-red complexion, and wearing brown-red or red robes.
Only a few statements mention the worship of Buddha, e.g. the Varahapurana says states that one desirous of beauty should worship him.
In some of the Puranas, he is described as having taken birth to "mislead the demons":
- mohanārthaṃ dānavānāṃ bālarūpī pathi-sthitaḥ । putraṃ taṃ kalpayām āsa mūḍha-buddhir jinaḥ svayam ॥
- tataḥ saṃmohayām āsa jinādyān asurāṃśakān । bhagavān vāgbhir ugrābhir ahiṃsā-vācibhir hariḥ ॥—attributed to Brahmanda Purana, quoted in Bhāgavatatātparya by Madhva, 1.3.28
Translation: To delude the demons, he [Lord Buddha] stood on the path in the form of a child. The foolish Jina (a demon), imagined him to be his son. Thus the lord Sri Hari [as avatara-buddha] expertly deluded Jina and other demons by his strong words of non-violence.
In the Bhagavata Purana Buddha is said to have taken birth to restore the devas to power:
- tataḥ kalau sampravṛtte sammohāya sura-dviṣām ।
- buddho nāmnāñjana-sutaḥ kīkaṭeṣu bhaviṣyati ॥—srimad-bhagavatam 1.3.24
Translation: Then, in the beginning of Kali-yuga, for the purpose of confusing the enemies of the devas, [he] will become the son of Anjana, Buddha by name, in the Kīkaṭas.
In many Puranas, the Buddha is described as an incarnation of Vishnu who incarnated in order to delude either demons or mankind away from the Vedic dharma. The Bhavishya Purana contains the following:
At this time, reminded of the Kali Age, the god Vishnu became born as Gautama, the Shakyamuni, and taught the Buddhist dharma for ten years. Then Shuddodana ruled for twenty years, and Shakyasimha for twenty. At the first stage of the Kali Age, the path of the Vedas was destroyed and all men became Buddhists. Those who sought refuge with Vishnu were deluded.
According to Wendy Doniger, the Buddha avatar, which occurs in different versions in various Puranas, may represent an attempt by orthodox Brahminism to slander the Buddhists by identifying them with the demons. Helmuth von Glasenapp attributed these developments to a Hindu desire to absorb Buddhism in a peaceful manner, both to win Buddhists to Vaishnavism and also to account for the fact that such a significant heresy could exist in India.
The times ascribed to one "Buddha" figure are contradictory and some put him in approximately 500 CE, with a lifetime of 64 years, describe him as having killed some persons, as following the Vedic religion, and having a father named Jina, which suggest that this particular figure might be a different person from Siddhārta Gautama.
- Bhagavata Purana, Canto 1, Chapter 3 - SB 1.3.24: "Then, in the beginning of Kali-yuga, the Lord will appear as Lord Buddha, the son of Anjana, in the province of Gaya, just for the purpose of deluding those who are envious of the faithful theist." ... SB 1.3.28: "All of the above-mentioned incarnations [avatars] are either plenary portions or portions of the plenary portions of the Lord [Krishna or Vishnu]"
- "in Sanskrit philosophical literature, 'āstika' means 'one who believes in the authority of the Vedas' or 'one who believes in life after death'. ('nāstika' means the opposite of these). The word is used here in the first sense." Satischandra Chatterjee and Dhirendramohan Datta. An Introduction to Indian Philosophy. Eighth Reprint Edition. (University of Calcutta: 1984). p. 5, footnote 1.
- Dasavatara stotra
- Lecture 1974 by founder of ISKCON - A. C. Bhaktivedanta Swami Prabhupada "Because people were addicted so much in violence, in killing the animals, therefore Buddha philosophy was needed"'
- Hinduism, in The World's Parliament of Religions, J. H. Barrows (Ed.), Vol. II, Chicago 1893, p. 978.
- Eastern Religions and Western Thought, New York 1969, pp. 326–7.
- Mahatma Gandhi and Buddhism
- McKean, Lise: Divine Enterprise. Gurus and the Hindu Nationalist Movement. Chicago University Press, 1996. Elst, Koenraad: Who is a Hindu (2001)
- Nagendra Kumar Singh (1997), "Buddha as depicted in the Purāṇas", Encyclopaedia of Hinduism, Volume 7, Anmol Publications PVT. LTD., pp. 260–275, ISBN 9788174881687, http://books.google.com/books?id=UG9-HZ5icQ4C&pg=PA260
- Singh, page 264.
- Bhagavata Purana 1.3.24
- Motilal Banarsidass, Delhi 1982.
- Dhere Ramchandra Chintaman, Shri Vitthal: ek maha samanvaya, Shri Vidya Prakashan, Pune, 1984 (Marathi)
- Singh, pp. 262–264
- Singh, p.267
- Wendy O'Flaherty, Origins of Evil in Hindu Mythology. University of California Press, 1976, page 203.
- O'Flaherty, page 200.
- von Glasenapp 1962 page 113, cited in O'Flaherty, page 206.
- Singh, p.266.
- Buddha as an Avatar of Vishnu at HinduWiki
- Buddha: The Refiner of Hinduism? (hinduism.about.com)
- The Buddha as an Avatar of Vishnu (article by A. Seshan from The Times of India)
- Mahatma Gandhi and Buddhism (pdf file)
- Buddhism, the Fulfilment of Hinduism, by Swami Vivekananda