Speaking in Italy, the Prime Minister said she was committed to a transitional period after the UK leaves the EU.
The NFU said steps described will provide stability for farm businesses and prepare the ground for both sides to make progress in Brexit negotiations.
But more details are needed if farmers and growers are to have the certainty to plan and invest in their businesses in the future, the union added.
NFU president Meurig Raymond said: "Farmers and growers are becoming increasingly alarmed at the prospect of a "no deal" departure from the EU. The resulting disruption to trade, access to labour and business stability would pose a fundamental threat to the viability of many of their businesses.
"The implementation period that the Prime Minister spoke of will be crucial if we are to reach a Brexit settlement that backs British farming, although we await further details on exactly how such a transition will work.
"We believe at least two years is needed to ensure a smooth Brexit, while also agreeing a future relationship between the EU and UK which recognises their mutual importance in terms of trade.
"With over 70% of our exports of food and non-alcoholic drinks being sent to EU markets, the NFU has been making the strongest case for a comprehensive free trade agreement between the EU and UK.
"We were pleased to hear the Prime Minister say there is no intention to impose tariffs where none currently exist, which the NFU takes as a strong commitment to securing a free trade deal with the EU.
"Any agreement should maintain as far as practicable the free flow of agri-food products between the EU and UK, and following today’s speech this remains a realistic prospect, although much now depends on proper progress being made in the negotiations.
During her speech the Prime Minister also said migrants would still be able to live and work in the UK but they would have to register with the authorities.
The NFU responded by saying the industry desperately needs more detail on how the immigration system will work both during and after the transition: "Vague pledges and offers are not enough if potential workers are to be reassured that they can legally take up the jobs on offer".
British Retail Consortium chief executive Helen Dickinson said: "We are pleased the Prime Minister has recognised that Brexit needs to work for consumers which means time to adapt new customs controls to avoid disruption and a final deal which avoids new tariffs at a time when household budgets are already squeezed.
"Our EU colleagues in stores and supply chains are part of the reason that British retailers are often able to deliver affordable and high-quality goods. The Prime Minister is right to offer a real guarantee to both EU workers and UK nationals in the EU-27 between 2019-2021, subject to a registration requirement.
"However, they still need practical details about the process for registration and securing their status, so the UK Government should negotiate with the EU Commission so that preferential reciprocal labour market access across industries like retail can be put in place for the post-implementation period.
"A period of implementation is vital to offer certainty for businesses and allow them to prepare. It provides welcome assurance that existing trading conditions are to remain in place based on the existing structure of EU rules and regulations. This will aid the free flow of goods in the transitional period post 2019.
"Businesses and consumers will share the aspiration of the deepest access to European markets in goods and services post-Brexit but clarity from both sides on exactly how this can be delivered and on what terms is essential in the coming weeks and months. Clarity together with creativity are required to deliver a deal that works for retail businesses and consumers."