A rogue elephant, who trampled 15 people to death in eastern India, has been shot dead in an elaborate hunt involving forest guards and sharpshooters.

The wild elephant, believed to be about 25-years-old, had killed four people in Bihar in March before it crossed over to neighbouring Jharkhand state where it crushed 11 people to death.

Forest authorities recently signed shooting orders for the tusker, which had so terrorised the locals that they fled their villages in the hilly forests of Jharkhand.

"In a challenging operation amid heavy rains, dense forests and low visibility, our team comprising 50 staff finally managed to track down the elephant on Friday evening," state chief forest wildlife conservator Lal Ratnakar Singh said.

"An expert hunter and sharpshooter was given the task to take the perfect aim, as we want to avoid a painful death for the animal. He fired the first shot on its forehead, and after it fell, fired another shot to confirm it was killed," he said.

The elephant was buried in the forest early on Saturday.

"It was unfortunate we had to kill the elephant but were forced to issue the shooting orders since it was wreaking havoc in the region. The villagers have heaved a sigh of relief," Singh added.

Attacks by wild elephants are common in India, and government reports say more than 300 people are killed each year by them. Many such elephants, who raze entire fields of precious crops, are also killed by angry villagers in retaliation.