The stock rose 2.5% in trading on Thursday.
Deere said May, 50 years old, will become the 10th CEO in the company's 182-year history.
May has been the company's president and chief operating officer since April and held various senior management positions since 2012. He first joined Deere in 1997.
May will also become a member of the board, effective immediately.
"John's record of success and proven leadership skills make him highly qualified to lead Deere and guide its success in the years ahead," Allen said in a statement. "His experience in precision agriculture, information technology, and overseas operations will be instrumental in driving the company's digitalization journey and extending its success in agricultural and construction equipment."
May became the company's chief information officer and president of the company's agricultural solutions division in 2012. Last year, he was named president of the company's worldwide agriculture and turf division.
Allen has been the CEO of Deere since August 2009 and chairman since February 2010.
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