Thompson left the BBC this autumn after almost eight years in charge, during which time he oversaw major international expansion at the corporation.
The New York Times appointed Thompson in August, citing his international and digital media experience as being valuable assets for the 161-year-old business. The company, which also includes the International Herald Tribune and the Boston Globe newspapers, posted revenues of $2.3bn (£1.47bn) in 2011.
However, Thompson starts at the time when the BBC is locked in one of the worst controversies of its history, which has already seen Thompson's successor, George Entwistle, quit after just 54 days in the job.
Entwistle opted to resign at the weekend after a Newsnight report led to former Tory Treasurer Lord McAlpine being wrongly linked to child abuse.
Even before starting at NYT, Thompson was accused by a senior writer at the paper of "appearing wilfully ignorant" over another scandal involving sex abuse allegations against ex-BBC star Jimmy Savile.
Respected journalist Joe Nocera questioned whether the New York Times owners, the Sulzberger family, had made the right choice in appointing Thompson.
Nocera felt certain that there was a "cover-up" involved in the controversial decision to drop a Newsnight investigation into Savile in December last year, when Thompson was still in charge of the BBC.
"Plainly, the answer is yes [there was a cover-up]. What is far less certain is how high the cover-up went," he wrote in late October.
Nocera challenged Thompson over why he did not request more details about the content and tone of the investigation when he was informed about it last year.
"Thompson winds up appearing wilfully ignorant, and it makes you wonder what kind of an organisation the BBC was when Thompson was running it - and what kind of leader he was. It also makes you wonder what kind of chief executive he'd be at the Times," he added.
Thompson began his career as a production trainee at the BBC in 1979 and then rose through the ranks to director of television, before leaving the corporation in 2002 to become chief executive of Channel 4.
He was appointed BBC director general in 2004, replacing Greg Dyke who had resigned following the Hutton Inquiry, and remained in the role until September 17 this year.
NYT chairman Arthur Sulzberger has always publicly given Thompson his backing as the right man for the job.
"Mark is a gifted executive with strong credentials whose leadership at the BBC helped it to extend its trusted brand identity into new digital products and services," he said in a statement in August.
Thompson said that it was a "privilege" to take on the role. He added: "I'm particularly excited to be coming to New York Times Company as it extends its influence digitally and globally."