The current director general of the BBC is set to leave his post and be succeeded by George Entwistle on September 17.
Times Company chairman Arthur Sulzberger Jr made the announcement this afternoon (August 14), with plans for Thompson to take over the role in November.
In a company statement, Thompson declared: "The New York Times is one of the world's greatest news providers and a media brand of immense future potential both in the US and around the world.
"It is a real privilege to be asked to join the Times Company as it embarks on the next chapter in its history."
The New York Times has been without a CEO since Janet Robinson departed in December 2011.
The paper is the third-largest in the US, and the New York Times website is the most popular newspaper site in the country, receiving 30 million hits a month.
However, the company is continuing to suffer huge losses as overall readership falls, and will be looking to apply Thompson's experience at the BBC in digital expansion and working with decreased budgets to their future development.
In May, Thompson came out to defend criticism of the BBC's diamond jubilee coverage to MPs, and last week publicly rejected reports that he had been "unhappy" with the BBC's London 2012 Olympics coverage.