Jones has sat on the Cello board for two years and will take over the reins from long-time chairman Allan Rich, who has stepped down.
The change was first announced in last month’s half-year results, when it reported a 9% rise in profits.
“The board wishes to wholeheartedly thank Allan Rich for his invaluable contribution to Cello over the years from its inception,” said chief executive Mark Scott.
“Chris knows the group and the healthcare industry well and can help guide the board through the group's next stage of growth and development.”
Jones was previously the chairman and chief executive of marketing group J Walter Thompson, which is owned by ad giant WPP PLC (LON:WPP).
Shares were down 0.9% to 114p in mid-afternoon trading on Monday.