Yes, the celebrations are mentioned in the Rudra Samhita of the Shiva Puran and it has both similarities as well as some differences with the current practices.
I am sharing the relevant text here in which Lord Shiva, after resuscitation of Ganesha, gives him the following blessing:
O Gaṇeśa, you are born in the first Prahara on the fourth day in the dark half of the Bhādra mouth at the auspicious hour of the moonrise. Since your form manifested itself from the good mind of Pārvatī, your excellent Vrata shall be performed on that Tithi itself or beginning from that day. It will be very auspicious and conducive to the achievement of all Siddhis. At the bidding of us both the Vrata shall be performed till the fourth day at the end of a year.
So, the first difference to note is that the text here states Chaturthi or fourth day of the Dark fortnight which is the Krishna Paksha but today we celebrate Ganesh Chaturthi on the Chaturthi of the Shukla Paksh or bright half of the month.
Secondly, it can be a fasting for a day there is also the other alternative of keeping it for a full year with the same ritual to be followed on every Chaturthi. The way to worship is detailed above and in the following passages:
Let those who yearn for unequalled happiness in the world worship you devoutly in various ways on the fourth day in accordance with the rules. On the fourth day of Lakṣmī in the month of Mārgaśīrṣa he shall perform early morning ablution and entrust the Vrata to the brahmins.
He shall perform worship with the Dūrvā grass and observe fast. After a Prahara has elapsed in the night the devotee shall take bath and worship the idol shall be made of metal, coral, white Arka flowers or clay. It shall be installed and worshipped by the devotee with all purity, with scents of various kinds, divine sandal paste and flowers.
A handful of Dūrvā grass having three knots and without roots shall be used for worship. The shoots shall be hundred and one in number. With twentyone the idol shall be worshipped. Gaṇeśa shall be adored with incense, lamps and different kinds of food-offerings.
After worshipping you with various articles of worship like betel etc. and eulogising you with hymns, the devotee shall worship the crescent moon. Afterwards, he shall feed the brahmins joyously with sweets with due honour. He himself shall take sweets and avoid salt.
Then the rites shall formally be dismissed. Then he shall remember Gaṇeśa. Thus the Vrata shall be concluded auspiciously.
So it seems the tradition of keeping the Ganpati idol for varying durations of odd days as is followed currently does not find mention in this scripture instead it is either a one day fast or a year-long one.
When thus the Vrata is duly completed in a year, the devotee shall perform the rite of formal dismissal for the completion of the Vrata. At my bidding twelve brahmins shall be fed. After placing a jar your image shall be worshipped.
After making the eight-petalled lotus diagram on the ground in accordance with Vedic injunctions a sacrifice shall be performed by the liberal people who have no disinclination to spend money. Two women and two students shall be worshipped and fed in front of the idol duly.
The devotee shall keep awake at night and perform worship in the morning. After that the rites of formal dismissal with the mantra “Kṣemāya Punarāgamanāya Ca.” (For welfare and return again) shall be performed.
The last sentence is especially relatable since even today we bid farewell to Ganpati with the words Pudhchya-varshi-lavkarya in Marathi or Agle baras tu jaldi aa in Hindi which translates to come back soon the next year!
Om Gam Ganapataye Namah! Hope this was helpful!