Page (above) will join the retailer's UK leadership team and report directly to group comms chief Jane Lawrie, who joined in October 2016 from Coca-Cola.
His remit is to "lead the ongoing programme of work to build trust in the Tesco business and brand across the UK and Ireland", the company said in a statement.
Previously a Freuds director leading on the agency's Asda and Mars accounts, Page was head of comms for airline Monarch from April 2016 until its collapse last year.
Lawrie said: "I am really looking forward to David joining the team. Not only does he have a wealth of experience in building and protecting reputation, he is a team player and a naturally progressive thinker. I am sure he will bring strength and depth to an already experienced and passionate team."
Page said: "I’m pleased to be joining at this important time for Tesco as it continues its turnaround, building loyalty, trust and reputation with its customers, suppliers, colleagues and shareholders."
He joins the firm at a busy time, with three major stories about the retailer coming out just this week. On Monday it announced a new UK CEO, who will join from wholesale group Booker at the same time as the merger of the two companies takes place. The following day, the four-month fraud trial of three former directors was abandoned after one of the trio had a heart attack. It is also facing what is reported to be the UK's largest ever equal pay claim, worth up to £4bn, it emerged on Wednesday.