Kellner will remain as honorary president and will continue working with 's media, political and other clients on a part-time basis.
He will also continue to represent YouGov in the media and at academic and other conferences, as well as playing an active role in the development of the company's polling business.
Kellner said: "The business continues to go from strength to strength however, on a personal level the time has come for me to step down from the board and from full-time work.
"This will allow me to continue with the stimulating work I do with YouGov and its clients as well as spending more time pursuing other unrelated projects."
Barker has been appointed to develop a qualitative business across the company, working closely with sector heads to deliver an integrated consulting offering to clients.
He has been in research for more than 20 years, most of the time as a qualitative specialist, including running qualitative units at BJM and Research International.
Barker has worked with UK and global clients in a range of product categories specialising in consumer understanding, communication/brand strategy and product innovation.
He said: "The opportunity to create a challenging and inventive qualitative business in such a dynamic company is unique and the panel represents a fabulous resource for a qualitative researcher frustrated by groups with the usual suspects."