Paul Allen, the world's seventh-richest person according to Forbes magazine, will make the investment through Global Vulcan Energy International, a wholly owned subsidiary of his personal investment vehicle, Vulcan Capital.
"We signed a memorandum of understanding on Thursday with the US energy firm, which will invest $1.6 billion in the next three years," said Mahmudur Rahman, executive chairman of Bangladesh's Board of Investment (BOI).
Vulcan will spend $900 million of Allen's $21 billion fortune building a number of gas-run power plants with a total 1800 megawatts (MW) of capacity - equivalent to almost half of existing national capacity.
The new plants will help meet new demand that is set to double to 7000 MW by 2007, and make up a power shortfall that already stands at between 500 MW and 700 MW.
Bangladesh is one of the poorest
countries in the world
Vulcan will also build two plants with the capacity to produce 140,000 tonnes of carbon-based organic fertiliser at a cost of $200 million, and set up a $500 million project to capture methane gas for power production from coal mines, Mahmudur said.
Allen's injection of funds will be the second biggest in Bangladesh behind a $2.5 billion project by India's Tata group.
Together, the two investments dwarf total foreign direct investment of three billion since Bangladesh became a nation in the early 1970s.
Half of Bangladesh's population lives below the poverty line, and the nation is home to the third highest number of poor people in the world behind India and China, according to the World Bank.
However, GDP grew by 6% last year and is set to grow a further 5% in the 2004/05 fiscal year.
Mahmudur said Vulcan's president, Ford Graham, and other senior company executives, visited proposed plant sites last
week and held meetings with Bangladeshi officials.
The firm will start a feasibility study in May, which will be completed within the next six months.