Mrs May said Keeping Nissan in the UK was regarded as vital to her hopes for a successful Brexit.
She said: "This is fantastic news for the UK. Nissan is at the heart of this country's strong automotive industry and so I welcome their decision to produce the Qashqai and a new model at their Sunderland plant.
"It is a recognition that the Government is committed to creating and supporting the right conditions for the automotive industry so it continues to grow - now and in the future.
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"This vote of confidence shows Britain is open for business and that we remain an outward-looking, world-leading nation.
"The Government will continue to work closely with employers and investors in creating a global Britain, a country where there are new opportunities for jobs and rewarding careers.
"Families across the North East will be delighted at this news today and I share in their enthusiasm for what this means not just for them, but for the whole of the UK."
The Sunderland plant, which has been active since 1986, employs almost 7,000 people, producing around 2,000 cars a day.
Nissan is part-owned by French manufacturer Renault, raising concerns that production could be moved to France to avoid any tariffs which might be introduced on exports to the EU if the UK leaves the single market in a so-called "hard Brexit".
Liberal Democrat Leader Tim Farron, however, slammed the Government over its handling of companies' concerns over Brexit.“The commitment to Sunderland by Nissan is obviously very welcome. Ensuring that jobs are protected at the plant is vital for Sunderland and our economy."However, it is utterly ridiculous that Theresa May is having to give special assurances to key manufacturers in order to deal with the Brexit fallout her government is creating. “What happens when other car companies come asking for special treatment? What about our other major industries - will they also be given protection? And what about the millions of small businesses who are being hit by a collapsing pound and severe economic uncertainty?"If the government was serious about protecting jobs in the UK, it would be fighting to remain part of the Single Market."
Business Secretary Greg Clark said: "The UK automotive sector has had a remarkable year - exporting over one million cars around the world and today's announcement underlines the confidence in the sector.
"The fact Nissan have not only made a long-term commitment to build the next generation Qashqai and X-Trail at Sunderland, but decided to upgrade their factory to a super-plant, manufacturing over 600,000 cars a year, is proof of the strength of the sector."