Stevenson, who took up the role last week, is the first person to officially step into the job since Potato Council became part of the new Agriculture & Horticulture Development Board (AHDB) in April.
His appointment follows the resignation in February of the previous permanent chairman, Janet Bainbridge. Businessman Dennis Heywood acted as interim chairman following Bainbridge's departure and stood down last week after Stevenson's appointment.
Farmer and qualified chartered accountant Stevenson has worked in various business and finance roles in food service, engineering and manufacturing companies.
He will continue to run his East Lothian-based business, Luffness Mains, which won the Tesco/Greenvale Scottish Potato Grower of the Year accolade in 2007.
He has also been appointed as a board member of the AHDB.
As Potato Council chairman, he will have responsibility for how the levy collected from the potato sector is spent for the sector's benefit.
AHDB chairman John Bridge, in welcoming the appointment, said: "I am delighted to have someone of Allan's calibre on board; he will be a real asset."
Stevenson, who is also a governor of the Scottish Crop Research Institute, said: "I look forward to working closely with the board of AHDB, and in particular with the excellent team at the Potato Council, whose value to the British potato industry is vital in strengthening the sector and ensuring its future success."
Stevenson will be paid £300 a day with an initial commitment of 172 days a year.