Robinson, aged 37, had previously been leading the marketing and sales around The Sun’s new paywalled Sun+ digital offering since the start of the year.
He takes over from Painter, who became marketing director with Sky Betting and Gaming.
Robinson joined News UK from BBC Worldwide in August 2010 as head of customer engagement, before becoming director of customer retention at the start of last year. He has also recently been involved in the new football season launch of The Sun’s Dream Team fantasy football league.
Katie Vanneck-Smith, News UK chief marketing officer, noted the "wealth of commercial and marketing acumen" he brings to the role.
She said: "In his three years working across the News UK estate, David has established himself as a well-respected member of the team.
"His passion and understanding of The Sun brand, a proven track record of innovative marketing, as well as his leadership and collaborative qualities – demonstrated in leading the launch of Sun+ – I am greatly excited by his appointment to the role."Follow @DurraniMix