At the end of the novel, we read:
The following evening was very wet: indeed, it poured down till day-dawn; and, as I took my morning walk round the house, I observed the master's window swinging open, and the rain driving straight in. He cannot be in bed, I thought: those showers would drench him through. He must either be up or out. But I'll make no more a do, I'll go boldly and look.
Having succeeded in obtaining entrance with another key, I ran to unclose the panels, for the chamber was vacant; quickly pushing them aside, I peeped in. Mr. Heathcliff was there—laid on his back. His eyes met mine so keen and fierce, I started; and then he seemed to smile. I could not think him dead: but his face and throat were washed with rain; the bed-clothes dripped, and he was perfectly still.
What has happened is that Nellie finds Heathcliff dead in his bed. He is soaked in rain. The "storm" in his soul is over. Heathcliff's entire life has been a storm. In the end, the rain has washed away his pain in this life. So, I believe it is a symbol of renewal. The season is springtime, which brings spring rain that gives new life to the earth. Perhaps Heathcliff will find his "new life" in another world, because his life in this world was a tortured life.
Nature is a major theme in this novel. The windswept moors in which it takes place, the dark of night in which supernatural events occur, the woods into which Catherine and Heathcliff escape (both as children and as adults), the rocks, the trees, the snowstorms, the rain. As it says here in the analysis on enotes:
The novel opens with a snowstorm, and ends with the flowering of spring, mirroring the passions that fuel the drama and the peace that follows its resolution.
Read more about the novel here on enotes.