The hymn is composed in Hamsadhvani raga (musical mode); however, in tradition of kritis, individual performers add their own variations in the tune as a part of improvisation.

"Vatapi Ganapatim" is a part of the series of hymns called Shodasha Ganapati kritis, a collection of songs dedicated to sixteen Ganesha icons located in shrines around Dikshitar's birthplace Thiruvarur.

As per oral tradition, the icon of Vatapi Ganapati was brought as war booty from the Chalukyan capital of Vatapi (presently known as Badami in northern Karnataka) by Paranjothi, the commander-in-chief of the Pallava king Narasimhavarman I (reign: 630–668 CE), following the conquest of Pallavas over the Chalukyas (642 CE).

Later, Paranjothi renounced his violent ways and became a Shaiva monk known as Siruthondar, is venerated as a Nayanar saint today.

[2][3] However, no written records substantiate the oral tradition; the Ganesha icon is missing from list of war booty brought by the Pallava general.

He resides in the Muladhara chakra and exists in four kinds of speech – Para, Pashyanti, Madhyama and Vaikhari.

[4][5] vāraṇāsyaṃ varapradaṃ śrī bhūtādi-saṃsēvita-caraṇam bhūta-bhautika-prapañca-bharaṇam vītarāgiṇaṃ vinata-yoginam (or) vītarāgiṇaṃ vinuta-yoginam viśvakāraṇaṃ vighnavāraṇam purā kumbha-saṃbhava-munivara prapūjitaṃ trikoṇa-madhyagatam murāri-pramukhādyupāsitam mūlādhāra-kṣētrasthitam parādi catvāri vāgātmakam praṇava-svarūpa vakratuṇḍam nirantaraṃ niṭila candrakhaṇḍam nija vāmakara vidhṛtekṣudaṇḍam karāmbuja-pāśa-bījā-pūram kaluṣa-vidūraṃ bhūtākāram harādi-guruguha-toṣita-bimbam haṃsadhvani bhūṣita hērambam Dikshitar composed Vatapi Ganapatim in Hamsadhvani raga (musical mode) of Carnatic music, which was created by his father Ramaswami Dikshitar (1735–1817) in 1790.

It is also associated with the notes Gandhara (ga) and Nishada (ni), the latter is often compared with an elephant's sound – thus suitable for the elephant-headed god.

Thus, Muthuswami Dikshitar may have digressed from his usual ragas and composed in Hamsadhvani, due to the Tantric associations with Ganesha.

Subbarama (1839–1906) received the knowledge of the songs from Balaswami, his grandfather and guardian by adoption, who was Muthuswami's younger brother.

[10] Although the piece is set in a well-defined raga, "every performance of "Vātāpi Gaṇapatim" is different, due to the importance of improvisation" in Carnatic music.

Iyer repeated the lines and introduced his own variations called sangatis, a characteristic of all kriti performers.

[8] In 1991, Amy Catlin noted that the hymn is traditionally sung first in many Carnatic music concerts in Chennai.

According to Amy Catlin, the fame of the hymn streams from its patron deity, Ganesha, who is a popular Hindu god as well as the melodious and simple music, which was composed in a newly created raga.