Under the PNG LNG agreement, MOL will charter two existing 177,000-cubic-metre capacity LNG carriers co-owned by Itochu Corporation.
MOL also entered into two heads of agreement for the construction and long-term charter of four LNG vessels for the PNG LNG and Gorgon LNG project.
The vessels are planned to be built in China with delivery expected in 2014-16.
First LNG from PNG LNG and Gorgon is expected in 2014.
The Exxon-operated PNG LNG project is expected to cost about $US15 billion ($A16.6 billion) with a production capacity of 6.6 million tonnes per annum of LNG.
The Chevron-operated Gorgon project consists of a three-train development on Barrow Island, off Western Australia, capable of producing 15MMtpa of LNG as well as a 300 terajoule per day domestic gas plant and pipeline to the mainland.
ExxonMobil is a partner in Gorgon.
MOL said it was looking forward to working with ExxonMobil and its partners in the years ahead.
"MOL will make the best use of its expertise, experience and resources throughout its global organisation to achieve the objectives of the two projects and to meet the high expectations of its new customers," it said.
The company has been providing transportation for large-scale LNG projects in the Asia-Pacific and Middle East regions for over 30 years.