Lister is expected to join BIS in the summer.
He has spent the past four years at DH where he led a number of major government comms programmes, including the domestic handling of Ebola, the Prime Minister’s Dementia Challenge and the development of the Stoptober stop-smoking drive.
Before joining DH, Lister spent 11 years at The Times as the newspaper’s health editor and in senior reporting roles.
In his new position at BIS, he will work on campaigns to support the growth of the UK business sector, the recruitment of three million apprentices by 2020, promotion of the National Living Wage and work with UKTI and the Cabinet Office on the GREAT Britain campaign.
Lister said: "It is a great privilege to be joining the communications team at BIS and its wider network of organisations at such an important period for driving forward the Government’s programme for the economy, job creation, EU reform and supporting innovation. After four-and-half fantastic years at the Department of Health, the time felt right for a new challenge, and I greatly look forward to taking up my role."
Alex Aiken, executive director of government comms at the Cabinet Office, added: "The communications work of BIS is key to the Government’s plans for this Parliament, and I am very pleased that Sam is taking on this role, as well as continuing our vital wider work to enhance the government communications profession. His leadership and experience taking forward some of the most demanding communications in Government over the past five years leaves him very strongly placed for these new challenges."