The property will have a private plunge pool and will face 280 metres of beach frontage with a fringe of coconut trees giving privacy.
Sri Lanka's east was a war zone until a 30-year war ended in 2009. The BOI said there was investments from France but did not give details.
"It reflects the peaceful situation in the country as well as the growing confidence on the part of the investor community to start hotel projects close to the former conflict areas," the BOI said in a statement.
"Tourism is one of the key economic sectors that Sri Lanka is targeting, since it provides many opportunities for investor in hotels and other tourism related activities."Styled as a boutique hotel, the property is expected to open for business in July 2014.