
Burns is promoted from his role as response-based marketing director, and will report to chief marketing officer Libby Chambers.
Jeppesen, who joined Barclays last year, is set to return to the US in August for family reasons. It is not known if he has a job to go to.
Former Washington Mutual marketer Jeppesen joined Barclays at the same time as commercial marketing director Richard French, who replaced former group brand and UK banking marketing director Jim Hytner.