Bruckner is moving to a new role at the privately owned energy drink's Austrian headquarters.
Carling, currently Red Bull marketing manager, will replace him from January and takes a place on the UK board.
Carling represented Red Bull as a student brand manager while he was at Cambridge from 1997 to 1999. In 1999 he joined the firm as assistant to UK managing director Harry Drnec. He has since worked in regional and trade marketing, before taking up the role of marketing manager 18 months ago.
Carling will oversee the direction of the brand in the UK, including its advertising account, worth around £6m.
The brand's trademark animated ads, which carry the strapline 'Red Bull gives you wings', are created by Kastner & Partners, with media planning and buying through AMS.