Roberts will succeed Richard Macdonald, who retires in late November.
NFU president Peter Kendall said: "He brings with him a wealth of experience and knowledge of our complex industry, is an experienced manager who has successfully led the AHDB through a period of massive change and shares our vision of why farming matters more than ever to the British economy and society.
"It is an exciting time to be involved in farming, with food security rising ever higher up the agenda, and I am looking forward to Kevin joining our strong and experienced team at the NFU."
NFU director of policy Martin Haworth will be taking up the post of acting director general on 26 November until Kevin Roberts starts.
Kevin Roberts said: "I am proud of what I have achieved at AHDB and it is a logical time to move on. I am really pleased to be joining the NFU; it is the key organisation in farming, has a great track record of achievements and has an exciting agenda of work ahead of it. I am really looking forward to working with everybody at the NFU on that agenda."
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