The appointment comes at a crucial time for the company as it looks at a number of ways of raising fresh capital.
Future, publisher of the Official PlayStation titles, said earlier this month it had abandoned talks about a possible sale of the company. Talks of a sale briefly boosted the company's battered share price.
The company abandoned the talks in favour of other options, including raising capital from existing or new shareholders, or an asset sale.
Bowman held the same post at Scottish Radio where he has worked since 1994. Prior to joining Scottish Radio, he worked for KPMG.
Scottish Radio said it has promoted Alan Wilson to replace him. Wilson is currently financial controller at the media group.
Greg Ingham, Future's chief executive, said, "John is a well-regarded media professional, [he] is well known in the City and his strong financial credentials will be of great benefit to Future Network. We are pleased to appoint someone of John's calibre as we move the group forward."