Norman will join the motor racing body on 14 August and report to managing director of commercial operations, Sean Bratches.
She has been at Virgin Media for five years, initially as head of advertising and online, adding sponsorship to her portfolio in 2014.
Before this, she spent seven years in marketing and communications roles at Honda, the last two as European communications manager.
Her achievements at Virgin include the "9.58 seconds" ad, starring Usain Bolt, which Campaign named as one of the best of 2016.
Bratches said: "Ellie’s appointment represents the latest addition to our expanding management team, aimed at increasing engagement with Formula One fans globally.
"Her previous experience across major automotive and media brands will help Ellie to drive Formula 1’s marketing strategy forward. We are excited to embrace new, fresh ideas from such an accomplished marketing industry expert."
Norman added: "The commercial potential of the brand is enormous and I can’t wait to work with Sean and the growing Formula One team to unlock new opportunities to engage with Formula One fans around the world."