(Reuters) - Nepal has given an Indian company permission to build a 900 megawatt hydropower plant, government officials said on Monday, as the Himalayan state looks to ease chronic energy shortages by opening up its rivers to its larger neighbor.

The two countries will sign an agreement for the $1.04 billion project, which provides Nepal with free electricity and India energy for its power-hungry economy, later this week when South Asian heads of state meet for a regional summit in Kathmandu, Nepal's Law Minister Narahari Acharya told Reuters.

"We have passed the Arun III agreement. It will be signed this week with the Indian company," said Acharya following a cabinet meeting where the project was approved.

Indian firms are investing billions to develop Nepal's hydropower potential, encouraged by an electricity trading pact signed between the two countries last month and pushed by Indian Prime Minister Narendra Modi.

Growing investment in Nepal's energy industry comes as New Delhi looks to grow its influence in its smaller neighbors, where China is increasingly active.

The project, which will be built by Satluj Jal Vidyut Nigam (SJVN) Limited, was originally cleared in 2008 but never implemented after Kathmandu lobbied for greater benefits.

Under the agreement SJVN will develop the plant on the Arun River in the country's east, and supply a fifth of generated electricity to Nepal for free, said Ghanashyam Ojha, external affairs chief at the Investment Board Nepal.

Nepal will earn $3.48 billion over 25 years in royalty, income and taxes from the plant, officials said, and will then take ownership of the project.

Indian firms are negotiating with the government for power plants that would produce a total of 8,250 MWs, officials in Nepal said, and Kathmandu estimates $7 billion will be invested in its hydropower industry over the next 5 years.

Nepal has the potential to generate 42,000 MW of hydropower but today produces 800 MW -- less than demand of 1,400 MW.