The story of Omkareshwar Jyotirlinga is described in the Puranas in this way
The first story
Once while touring Naradji reached the Vindhyachal mountain. There the mountain king Vindhyachal welcomed Narada and saying that I am endowed with all qualities, I have everything, all kinds of wealth, reached before Narada.
Hearing the proud words of Vindhyachal, Narada stood silently with long breaths. Then Vindhyachal asked Narada what deficiency he saw in me. You took a long breath when you saw it. Then Narada said, “You have everything, but you are not higher than Mount Sumeru.
The part of that mountain has reached the realm of the gods, and the part of your summit will never reach there. Saying this, Narada left the place. But Vindhyachal, who was standing there, felt very sad and began to grieve heartily.
It was then that he decided to worship Lord Shiva. At the place where the real Omkar is present, he installed the Shivling and worshiped continuously for 6 months with a happy heart. Thus Lord Shiva became very pleased and appeared there. He said, “I’m very happy. You can ask for any gift.
Then Vindhya said, “You are really pleased with me, so give me wisdom which will prove your work.” Then Lord Shiva said to him, “I give you boon that the kind of work you want to do will be accomplished.
After giving the boon some gods and sages also came there. They all worshiped Lord Shiva and prayed, “O Lord! You’ll be here forever.
Lord Shiva was very pleased. Lord Shiva, who did public welfare, accepted them and that Omkar Linga was divided into two genders. The earthly linga created by the Vindhyas is known as the Parameswara linga and the linga established by Lord Shiva is called the Omkara linga. Parameswara Linga is also called Amaleswara Linga and since then both these Shivalingas became famous in the world.
Another story
King Mandhata had worshipped Lord Shiva by doing severe penance on this mountain. Lord Shiva was very pleased with the penance and appeared. Then King Mandhata asked Lord Shiva to be seated here forever.
Since then, Lord Shiva is worshipped here. That is why this city is also called Omkar-Mandhata. There are 68 pilgrimage sites in this region and it is said that 33 crore gods and goddesses reside here. There is a special significance of bathing in Narmada here. Only the darshan of Narmada ji removes all your sins.
The story
Once upon a time there was a war between the gods and the demons. The demons defeated the gods. The Devas could not bear this and in desperation prayed to Lord Shiva and offered prayers. Seeing his devotion, Lord Shiva was extremely pleased and Omkareshwar was installed as Jyotirlinga and defeated the demons.
In this temple, Lord Shiva is worshipped by worshipping Lord Kubera. He was a devotee of Lord Shiva. Pleased with his devotion, Lord Shiva made him a rich man. Lord Shiva had created the Kaveri river from his hair, from which Kuber had bathed. The Kaveri River flows around the Omkar mountain and joins the Narmada River. This is called the confluence of Narmada and Kaveri.
There is also a story about Adi Shankara Cave that Adi Shankara met his Guru Govind Padacharya in this cave. Even today this cave is located below the Shiva temple in which the image of Adi Shankara is seen. The problems of the devotees are removed as soon as they step on the land of this holy place. Just by having darshan of Lord Shiva here, it seems that one has darshan of Lord Shiva.
It is described in Chapter 18 of the Kotirudrasamhita of the Shiva Purana.