He is leaving by mutual consent on 18 December.
Lawson's responsibilities for digital will be overseen by chief operating officer Clive Dickens. His marketing responsibilities will be taken up by head of marketing Clare Baker, and head of communications Cat Macdonald will take over his communications role.
Lawson joined Absolute shortly after the station, then Virgin Radio, was bought by the Times of India last year.
Alongside the launch of Absolute Radio in September 2008, he was involved in the recent launches of the digital stations Absolute 80's and dabbl, as well as the website Compare My Radio.
Dickens will work with digital media editor Anthony Abbott and lead designer and developer Duncan Amey on Absolute's digital strategy. Dickens said Absolute Radio was now "firmly on its path to being a music and entertainment brand with audio at its core" and Lawson had played a very important part in that evolution.