Shareholders Tuesday voted for him to replace Le Thi Bang Tam, who resigned from the job after nearly seven years.
Phuc, 63, was the legislature’s general secretary from 2016 until November last year, when he retired.
He had earlier been a member of the Party Central Committee and head of the National Assembly Office.
Vinamilk shareholders also voted for Mai Kieu Lien to continue as CEO for the next five years.
Lien has said the company’s revenues could grow to VND86 trillion by 2025 (up 33 percent from this year's target) as average spending on dairy products in Vietnam remain low compared to countries in its neighborhood.