The appointment concludes an eight-month search for a new chief at the paper following the exit of Janet Robinson in December. Robinson oversaw the paper's launch of its metered paywall, which has performed better than expected. Last month The New York Times reported a 12 per cent rise in digital subscriptions to more than 500,000.
Thompson is due to leave the BBC next month after eight years in the role and 33 years at the BBC, having joined the corporation in 1979 as a production trainee. He is being succeeded by George Entwistle, who was appointed in July.
He will take up his role in New York in November and will report to chairman Arthur Sulzberger.