David McNally, the club's chief executive, and Stephan Phillips have been appointed alongside Bowkett, who resigned from his role of chairman of construction company Redrow earlier this week.
In a statement the club's major shareholders Delia Smith and Michael Wynn Jones said: "The foundations are now in place to enable us to get to where we want to be.
"This new board is very experienced and ambitious and now it's all about getting on with the job."
Mr Bowkett said: "Our task at Norwich is a simple one - we must start winning football matches. It will be the board's responsibility to ensure that we have the appropriate resources to do that, both human and financial."