ISBA represents more than 400 UK advertisers and the director of media's role is to work with media owners and agencies at a time when digital, particularly online brand safety, viewability and measurement, have shot to the top of the agenda.
Phil Smith, the director-general of ISBA, thanked Finney for his "significant contribution" but said he wanted to appoint Chester because he can "put the zing into our digital and data leadership".
He said: "Steve’s appointment reflects ISBA’s commitment to continue to strengthen its offering for digital advertisers."
Chester was director of data and industry programmes at the IAB, the trade body for internet advertising, until earlier this year and has also worked at Microsoft.
Finney brought broader experience of the ad industry as a former marketer at Orange and an agency executive at Carat and MPG.
He joined in April 2016, before Phil Smith took over as director-general of ISBA at the start of this year.
Smith has shaken up the trade body in a bid to rejuvenate the organisation and a number of executives have departed.
Finney is expected to seek a new role in the media industry.
His departure comes as a surprise. His predecessor, Bob Wootton, held the role for 20 years.
Smith said: "I’m delighted to welcome Steve to the ISBA team. His digital credentials and industry experience make him uniquely qualified to lead in the rapidly changing media environment.
"A big thank you is also due to Mark Finney, who has made a real impact on ISBA. We wish him every success in the future."