Whiting was already at Sixfields as their company secretary and financial director.
“I am pleased to appoint James into this role,” said Cardoza.
“James has been fulfilling the role unofficially for a while now and I believe the time is right to make that official.”
The Cobblers finished 12th in League Two, 10 points adrift of the play-offs under boss Chris Wilder and Whiting hopes for a successful future.
“It is a great honour for me to officially take up the post of chief executive at the club,” he added.
“I will be working extremely hard with the chairman, the board, Chris Wilder and all of the staff to ensure that we fulfil our huge potential as a club and I am excited about the future of Northampton Town.”