Irandam Ulagam is about two stories which unfold concurrently in two different planets – our Earth and an unnamed exoplanet.[2] On earth a timid medical student Ramya who has a crush on an academic mathematician Madhu Balakrishnan, asks him out. He initially refuses her proposal for marriage as his father has a disability, needing his full attention and care. Later, Madhu gradually reciprocates Ramya's love seeing her caring nature and proposes marriage. But, she reluctantly rejects his proposal as her family has already arranged her marriage. While on a trip to Goa, Madhu wins Ramya's heart while her fiancé abruptly cancels the marriage citing dowry as the reason. She suddenly dies in a freak accident, and this is followed by Madhu's paralysed father's death too. Depressed by the sudden twin tragedies, Madhu becomes a vagabond in Goa. He sees an apparition of his dead father that tells him death is an illusion. Later, at a local tourist spot, he follows an empty car to a hilltop and tries to commit suicide. He gets injured and faints while trying to drive the car.

The story moves parallel in the alternate world in a relatively primitive kingdom which protects the immortal Amma. The son of a noble military commander, Maravan, falls in love with a working class orphan, Varna. Maravan, though fearless, does not take an interest in martial arts and roams around the kingdom drinking with his friends. Varna, on the other hand, is interested in a military career though she picks and packs wild mushrooms to eke out a living. She also has the desire to protect Amma from the enemies of the kingdom. While gatecrashing a military admissions exam for Amma's protection, the tyrant king condemns Varna to his harem. Maravan pleads with the king to release Varna, and the king, in return, challenges Maravan to get hold of a lion's skin within three days. Maravan, though inexperienced, fights with the lion that has never been conquered until then and gets Varna released. At the behest of the king, Varna is forced to marry Maravan, which goes against her free will. So, she tries to commit suicide after assaulting the king. But Amma saves her, and the riled king exiles her to the forest. Depressed, Maravan tries to commit suicide in vain. Taunted by new military recruits, Maravan climbs a sacred mountain called Swamimalai.

Meanwhile, with the special powers of Amma, an inter-planetary portal opens briefly between Maravan in Swamimalai and Madhu in Goa. Maravan rescues the fainted Madhu from the car and takes him to Amma for treatment. People of the kingdom celebrate Madhu mistake him for an angel. Enemies lay siege to the kingdom and try to kidnap Amma, but intoxicated Maravan fights them off with the help of Varna, who returns from the forest. When Madhu looks at Varna (who looks like Ramya), flowers begin to bloom in the kingdom for the first time. But the timid people force Varna back into the forests. Later Maravan's bravery is rewarded by his father and king, who admits him into military service. Maravan, with new-found confidence, goes into the forest to meet Varna with food and blankets. But she rejects him again. Madhu, too goes into the forest to meet Varna. This time, Varna accepts his friendship. Marvan gets jealous of Madhu. A stormy night forces Varna to eventually return to the kingdom from the forest. The enemies of the kingdom capture Amma while the irate king sends Maravan for execution for illegally housing Varna. Maravan is captured by the enemy troops while abducting Amma. Madhu and Varna set out through the forest to find Maravan and Amma. Varna eventually realises that she had fallen in love with her husband Maravan after hearing about Ramya. Maravan bravely wipes out the entire army of the enemy and escapes with Amma on a boat. But Madhu is drowned in combat. Amma stops Varna and Maravan from saving him. Then an inter-planetary portal opens briefly again, and Madhu lands in another unnamed exoplanet where he finally meets his soulmate Ramya look-alike again. He earnestly asks her if she is single. Finally, he realises that it is his true destiny.