Clyne will report to CEO and founder Solly Solomou in a newly created role for the company behind digital brands TheLADbible, TheSPORTbible, Pretty52 and others.
He is tasked with driving the group's strategic growth and leading its day-to-day operations. Clyne begins his new role on 4 July.
With offices in London and Manchester and 100 staff, TheLADbible Group was created in 2012 and claims to reach more than 400 million people a month via a range of social platforms and its own website. Half of UK males aged 16-24 follow the brand in one form or another.
Clyne has been in his current Weber role since January 2015, having previously been global commercial director at TVC Group and later international MD when it was acquired by The Economist Group in 2012. Before TVC, he worked at numerous agencies including Cheetham Bell JWT, Geronimo Communications and Kindred.
He said he had an opportunity to "hugely scale this business across categories and borders".
Solomou said: "Adam brings a breadth of operational and digital experience that will help take TheLADbible Group to the next stage of our evolution. We are excited to bring someone of his calibre and maturity into the business. He will help us build on a period of strong growth."