Peters will take up the role in September when Dodd departs the charity to join Kaper in a newly created director role.
In her nine years at Cancer Research UK, Peters has worked on a range of campaigns including Race for Life and Stand up to Cancer.
She will be responsible for a team of 14, work closely with Aaron Eccles who leads on the charity’s social media and report to Carolan Davidge, director of comms at Cancer Research UK.
Davidge said: "Laura is an invaluable member of the team who leads her teams to achieve brilliant results on all her campaigns. We look forward to welcoming her into her new role this September."