The laboratory, which oversees measurement standards in UK industry and carries out research in partnership with the academy, has been operated by the private firm Serco since 1995.
However, in a written ministerial statement on Tuesday, universities and science minister David Willetts said he had decided not to renew Serco's contract when it runs out in March 2014 because the lab, and its west London site, "provide opportunities which would be difficult to realise under an extension of the current contract".
"The National Physical Laboratory is a crucial UK asset and we can be proud of its continued record as one of the top three national measurement institutes in the world. I want to strengthen both fundamental research and engagement with business by applying measurement science to support innovation and growth," he said.
The key, he added, would be to form a "strategic alliance" with one or more academic partners - possibly from overseas.
He said such a partnership would allow for "the possible formation of a dedicated applied science postgraduate institute" at the centre of "a science and innovation campus with a focus on measurement science for industry".
"Such a structure would provide both the long-term commitment that partners will be looking for and the impartiality and stability that industry and international bodies value," he said.