The former leader "will be responsible for curating and overseeing the strategic guidance" the board provides to Afiniti, the Guardian quoted the statement as saying on Friday.
The position represents one of Cameron's most prominent appointments since he stood down as Prime Minister in 2016 following the Brexit referendum. He has previously taken a number of roles at not-for-profit organisations and has a memoir, For the Record, due out later this year.
Cameron said he was "delighted" to take the job working on "transforming the future of customer service and interpersonal communications".
The advisory board features an array of high-profile figures including John Browne, former chief executive of BP and Francois Fillon, the former prime minister of France.
Afiniti was set up by the US-Pakistani entrepreneur Zia Chishti and specialises in the use of AI in call centres.
Since his resignation, Cameron has become President of Alzheimer's Research UK, chair of the National Citizen Service's board of patrons and chair of the LSE-Oxford commission on state fragility.
Chishti, the chair and chief executive of Afiniti, said the company was "delighted" at Cameron's appointment. "David's deep personal commitment to this issue makes him perfectly placed to lead our advisory board and support Afiniti in our next stage of growth."
( With inputs from IANS )